@inproceedings{54725,
  author       = {{Wedekind, Lisa and Pollmeier, Pascal and Fechner, Sabine}},
  booktitle    = {{Frühe naturwissenschaftliche Bildung}},
  editor       = {{van Vorst, Helena}},
  location     = {{Hamburg}},
  pages        = {{754--757}},
  title        = {{{Analyse der Analogiebildung in kontextorientierten Lernumgebungen}}},
  volume       = {{44}},
  year         = {{2024}},
}

@inbook{56162,
  abstract     = {{<jats:p>Die Autorinnen untersuchen im Rahmen ihrer Prä-Post-Studie mit Viertklässlern, ob der Modellierungsprozess durch analoges Schließen zwischen mehreren Phänomenen unterstützt werden kann, und ob chemische Konzepte zum Thema Löslichkeit erlernt werden können. Die Ergebnisse zeigen, dass Grundschüler*innen ihre mentalen Modelle in einem Modell ausdrücken und teilweise revidieren können. In einigen Fällen werden die Modelle reflektiert und Grenzen erkannt. (DIPF/Orig.)</jats:p>}},
  author       = {{Elsner, Julia and Tenberge, Claudia and Fechner, Sabine}},
  booktitle    = {{In Alternativen denken - Kritik, Reflexion und Transformation im Sachunterricht}},
  editor       = {{Egger, Christina and Neureiter, Herbert and Peschel, Markus and Goll, Thomas}},
  isbn         = {{9783781526235}},
  pages        = {{83--92}},
  publisher    = {{Verlag Julius Klinkhardt}},
  title        = {{{Analyse des Modellierprozesses von Grundschüler*innen zum Thema Löslichkeit}}},
  doi          = {{10.35468/6077-08}},
  year         = {{2024}},
}

@inproceedings{62954,
  author       = {{Ponath, Jonas and Pollmeier, Pascal and Fechner, Sabine}},
  booktitle    = {{Jahrestagung der Gesellschaft für Didaktik der Chemie und Physik e.V.}},
  keywords     = {{Digital, Digitalisierung, Künstliche Intelligenz, KI, Messsensoren, Lehrkräfte, Chemie, Kompetenzen}},
  location     = {{Bochum}},
  title        = {{{Erhebung und Förderung digitalisierungsbezogener Kompetenzen von Chemielehrkräften}}},
  year         = {{2024}},
}

@inbook{57768,
  author       = {{Elsner, Julia and Buyken, Anette E. and Schulte, Eva Andrea and Fechner, Sabine}},
  booktitle    = {{Lehkräftebildung in der digitalen Welt - Zukunftsorientierte Forschungs- und Praxisperspektiven}},
  editor       = {{Herzig, Bardo and Eickelmann, Birgit and Schwabl, Franszika and Schulze, Johanna and Niemann, Jan}},
  pages        = {{191--202}},
  publisher    = {{Waxmann}},
  title        = {{{Der digitale Erste-Hilfe-Koffer - Unterstützung von Studierenden der Ernährungslehre im Bereich Chemie}}},
  volume       = {{1}},
  year         = {{2024}},
}

@book{57441,
  editor       = {{Höink, Dominik and Meyer, Andreas}},
  isbn         = {{978-3-8288-4979-2}},
  publisher    = {{Tectum}},
  title        = {{{Music and Religions in the 21st Century}}},
  volume       = {{1}},
  year         = {{2024}},
}

@article{63264,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>In a smoothly bounded convex domain <jats:inline-formula id="j_ans-2023-0131_ineq_001">
                     <jats:alternatives>
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                           <m:mi mathvariant="normal">Ω</m:mi>
                           <m:mo>⊂</m:mo>
                           <m:msup>
                              <m:mrow>
                                 <m:mi mathvariant="double-struck">R</m:mi>
                              </m:mrow>
                              <m:mrow>
                                 <m:mi>n</m:mi>
                              </m:mrow>
                           </m:msup>
                        </m:math>
                        <jats:tex-math>
${\Omega}\subset {\mathbb{R}}^{n}$
</jats:tex-math>
                        <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ans-2023-0131_ineq_001.png"/>
                     </jats:alternatives>
                  </jats:inline-formula> with <jats:italic>n</jats:italic> ≥ 1, a no-flux initial-boundary value problem for<jats:disp-formula id="j_ans-2023-0131_eq_999">
                     <jats:alternatives>
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block" overflow="scroll">
                           <m:mfenced close="" open="{">
                              <m:mrow>
                                 <m:mtable class="cases">
                                    <m:mtr>
                                       <m:mtd columnalign="left">
                                          <m:msub>
                                             <m:mrow>
                                                <m:mi>u</m:mi>
                                             </m:mrow>
                                             <m:mrow>
                                                <m:mi>t</m:mi>
                                             </m:mrow>
                                          </m:msub>
                                          <m:mo>=</m:mo>
                                          <m:mi mathvariant="normal">Δ</m:mi>
                                          <m:mfenced close=")" open="(">
                                             <m:mrow>
                                                <m:mi>u</m:mi>
                                                <m:mi>ϕ</m:mi>
                                                <m:mrow>
                                                   <m:mo stretchy="false">(</m:mo>
                                                   <m:mrow>
                                                      <m:mi>v</m:mi>
                                                   </m:mrow>
                                                   <m:mo stretchy="false">)</m:mo>
                                                </m:mrow>
                                             </m:mrow>
                                          </m:mfenced>
                                          <m:mo>,</m:mo>
                                          <m:mspace width="1em"/>
                                       </m:mtd>
                                    </m:mtr>
                                    <m:mtr>
                                       <m:mtd columnalign="left">
                                          <m:msub>
                                             <m:mrow>
                                                <m:mi>v</m:mi>
                                             </m:mrow>
                                             <m:mrow>
                                                <m:mi>t</m:mi>
                                             </m:mrow>
                                          </m:msub>
                                          <m:mo>=</m:mo>
                                          <m:mi mathvariant="normal">Δ</m:mi>
                                          <m:mi>v</m:mi>
                                          <m:mo>−</m:mo>
                                          <m:mi>u</m:mi>
                                          <m:mi>v</m:mi>
                                          <m:mo>,</m:mo>
                                          <m:mspace width="1em"/>
                                       </m:mtd>
                                    </m:mtr>
                                 </m:mtable>
                              </m:mrow>
                           </m:mfenced>
                        </m:math>
                        <jats:tex-math>
$$\begin{cases}_{t}={\Delta}\left(u\phi \left(v\right)\right),\quad \hfill \\ {v}_{t}={\Delta}v-uv,\quad \hfill \end{cases}$$
</jats:tex-math>
                        <jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ans-2023-0131_eq_999.png"/>
                     </jats:alternatives>
                  </jats:disp-formula>is considered under the assumption that near the origin, the function <jats:italic>ϕ</jats:italic> suitably generalizes the prototype given by<jats:disp-formula id="j_ans-2023-0131_eq_998">
                     <jats:alternatives>
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block" overflow="scroll">
                           <m:mi>ϕ</m:mi>
                           <m:mrow>
                              <m:mo stretchy="false">(</m:mo>
                              <m:mrow>
                                 <m:mi>ξ</m:mi>
                              </m:mrow>
                              <m:mo stretchy="false">)</m:mo>
                           </m:mrow>
                           <m:mo>=</m:mo>
                           <m:msup>
                              <m:mrow>
                                 <m:mi>ξ</m:mi>
                              </m:mrow>
                              <m:mrow>
                                 <m:mi>α</m:mi>
                              </m:mrow>
                           </m:msup>
                           <m:mo>,</m:mo>
                           <m:mspace width="2em"/>
                           <m:mi>ξ</m:mi>
                           <m:mo>∈</m:mo>
                           <m:mrow>
                              <m:mo stretchy="false">[</m:mo>
                              <m:mrow>
                                 <m:mn>0</m:mn>
                                 <m:mo>,</m:mo>
                                 <m:msub>
                                    <m:mrow>
                                       <m:mi>ξ</m:mi>
                                    </m:mrow>
                                    <m:mrow>
                                       <m:mn>0</m:mn>
                                    </m:mrow>
                                 </m:msub>
                              </m:mrow>
                              <m:mo stretchy="false">]</m:mo>
                           </m:mrow>
                           <m:mo>.</m:mo>
                        </m:math>
                        <jats:tex-math>
$$\phi \left(\xi \right)={\xi }^{\alpha },\qquad \xi \in \left[0,{\xi }_{0}\right].$$
</jats:tex-math>
                        <jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ans-2023-0131_eq_998.png"/>
                     </jats:alternatives>
                  </jats:disp-formula>By means of separate approaches, it is shown that in both cases <jats:italic>α</jats:italic> ∈ (0, 1) and <jats:italic>α</jats:italic> ∈ [1, 2] some global weak solutions exist which, inter alia, satisfy<jats:disp-formula id="j_ans-2023-0131_eq_997">
                     <jats:alternatives>
                        <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block" overflow="scroll">
                           <m:mi>C</m:mi>
                           <m:mrow>
                              <m:mo stretchy="false">(</m:mo>
                              <m:mrow>
                                 <m:mi>T</m:mi>
                              </m:mrow>
                              <m:mo stretchy="false">)</m:mo>
                           </m:mrow>
                           <m:mo>≔</m:mo>
                           <m:munder>
                              <m:mrow>
                                 <m:mtext>ess sup</m:mtext>
                              </m:mrow>
                              <m:mrow>
                                 <m:mi>t</m:mi>
                                 <m:mo>∈</m:mo>
                                 <m:mrow>
                                    <m:mo stretchy="false">(</m:mo>
                                    <m:mrow>
                                       <m:mn>0</m:mn>
                                       <m:mo>,</m:mo>
                                       <m:mi>T</m:mi>
                                    </m:mrow>
                                    <m:mo stretchy="false">)</m:mo>
                                 </m:mrow>
                              </m:mrow>
                           </m:munder>
                           <m:msub>
                              <m:mrow>
                                 <m:mo>∫</m:mo>
                              </m:mrow>
                              <m:mrow>
                                 <m:mi mathvariant="normal">Ω</m:mi>
                              </m:mrow>
                           </m:msub>
                           <m:mi>u</m:mi>
                           <m:mrow>
                              <m:mo stretchy="false">(</m:mo>
                              <m:mrow>
                                 <m:mo>⋅</m:mo>
                                 <m:mo>,</m:mo>
                                 <m:mi>t</m:mi>
                              </m:mrow>
                              <m:mo stretchy="false">)</m:mo>
                           </m:mrow>
                           <m:mi>ln</m:mi>
                           <m:mo>⁡</m:mo>
                           <m:mi>u</m:mi>
                           <m:mrow>
                              <m:mo stretchy="false">(</m:mo>
                              <m:mrow>
                                 <m:mo>⋅</m:mo>
                                 <m:mo>,</m:mo>
                                 <m:mi>t</m:mi>
                              </m:mrow>
                              <m:mo stretchy="false">)</m:mo>
                           </m:mrow>
                           <m:mo>&lt;</m:mo>
                           <m:mi>∞</m:mi>
                           <m:mspace width="2em"/>
                           <m:mtext>for all </m:mtext>
                           <m:mi>T</m:mi>
                           <m:mo>&gt;</m:mo>
                           <m:mn>0</m:mn>
                           <m:mo>,</m:mo>
                        </m:math>
                        <jats:tex-math>
$$C\left(T\right){:=}\underset{t\in \left(0,T\right)}{\text{ess\,sup}}{\int }_{{\Omega}}u\left(\cdot ,t\right)\mathrm{ln}u\left(\cdot ,t\right){&lt; }\infty \qquad \text{for\,all\,}T{ &gt;}0,$$
</jats:tex-math>
                        <jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ans-2023-0131_eq_997.png"/>
                     </jats:alternatives>
                  </jats:disp-formula>with sup<jats:sub>
                     <jats:italic>T</jats:italic>&gt;0</jats:sub>
                  <jats:italic>C</jats:italic>(<jats:italic>T</jats:italic>) &lt; ∞ if <jats:italic>α</jats:italic> ∈ [1, 2].</jats:p>}},
  author       = {{Winkler, Michael}},
  issn         = {{2169-0375}},
  journal      = {{Advanced Nonlinear Studies}},
  number       = {{3}},
  pages        = {{592--615}},
  publisher    = {{Walter de Gruyter GmbH}},
  title        = {{{A degenerate migration-consumption model in domains of arbitrary dimension}}},
  doi          = {{10.1515/ans-2023-0131}},
  volume       = {{24}},
  year         = {{2024}},
}

@article{63248,
  abstract     = {{<jats:title>Abstract</jats:title>
          <jats:p>The Navier–Stokes system <jats:disp-formula>
              <jats:alternatives>
                <jats:tex-math>$$\begin{aligned} \left\{ \begin{array}{l} u_t + (u\cdot \nabla ) u =\Delta u+\nabla P + f(x,t), \\ \nabla \cdot u=0, \end{array} \right. \end{aligned}$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mtable>
                      <mml:mtr>
                        <mml:mtd>
                          <mml:mfenced>
                            <mml:mrow>
                              <mml:mtable>
                                <mml:mtr>
                                  <mml:mtd>
                                    <mml:mrow>
                                      <mml:msub>
                                        <mml:mi>u</mml:mi>
                                        <mml:mi>t</mml:mi>
                                      </mml:msub>
                                      <mml:mo>+</mml:mo>
                                      <mml:mrow>
                                        <mml:mo>(</mml:mo>
                                        <mml:mi>u</mml:mi>
                                        <mml:mo>·</mml:mo>
                                        <mml:mi>∇</mml:mi>
                                        <mml:mo>)</mml:mo>
                                      </mml:mrow>
                                      <mml:mi>u</mml:mi>
                                      <mml:mo>=</mml:mo>
                                      <mml:mi>Δ</mml:mi>
                                      <mml:mi>u</mml:mi>
                                      <mml:mo>+</mml:mo>
                                      <mml:mi>∇</mml:mi>
                                      <mml:mi>P</mml:mi>
                                      <mml:mo>+</mml:mo>
                                      <mml:mi>f</mml:mi>
                                      <mml:mrow>
                                        <mml:mo>(</mml:mo>
                                        <mml:mi>x</mml:mi>
                                        <mml:mo>,</mml:mo>
                                        <mml:mi>t</mml:mi>
                                        <mml:mo>)</mml:mo>
                                      </mml:mrow>
                                      <mml:mo>,</mml:mo>
                                    </mml:mrow>
                                  </mml:mtd>
                                </mml:mtr>
                                <mml:mtr>
                                  <mml:mtd>
                                    <mml:mrow>
                                      <mml:mrow/>
                                      <mml:mi>∇</mml:mi>
                                      <mml:mo>·</mml:mo>
                                      <mml:mi>u</mml:mi>
                                      <mml:mo>=</mml:mo>
                                      <mml:mn>0</mml:mn>
                                      <mml:mo>,</mml:mo>
                                    </mml:mrow>
                                  </mml:mtd>
                                </mml:mtr>
                              </mml:mtable>
                            </mml:mrow>
                          </mml:mfenced>
                        </mml:mtd>
                      </mml:mtr>
                    </mml:mtable>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:disp-formula>is considered along with homogeneous Dirichlet boundary conditions in a smoothly bounded planar domain <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$\Omega $$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mi>Ω</mml:mi>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>. It is firstly, inter alia, observed that if <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$T&gt;0$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>T</mml:mi>
                    <mml:mo>&gt;</mml:mo>
                    <mml:mn>0</mml:mn>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> and <jats:disp-formula>
              <jats:alternatives>
                <jats:tex-math>$$\begin{aligned} \int _0^T \bigg \{ \int _\Omega |f(x,t)| \cdot \ln ^\frac{1}{2} \big (|f(x,t)|+1\big ) dx \bigg \}^2 dt &lt;\infty , \end{aligned}$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mtable>
                      <mml:mtr>
                        <mml:mtd>
                          <mml:mrow>
                            <mml:msubsup>
                              <mml:mo>∫</mml:mo>
                              <mml:mn>0</mml:mn>
                              <mml:mi>T</mml:mi>
                            </mml:msubsup>
                            <mml:mrow>
                              <mml:mo>{</mml:mo>
                            </mml:mrow>
                            <mml:msub>
                              <mml:mo>∫</mml:mo>
                              <mml:mi>Ω</mml:mi>
                            </mml:msub>
                            <mml:mrow>
                              <mml:mo>|</mml:mo>
                              <mml:mi>f</mml:mi>
                              <mml:mrow>
                                <mml:mo>(</mml:mo>
                                <mml:mi>x</mml:mi>
                                <mml:mo>,</mml:mo>
                                <mml:mi>t</mml:mi>
                                <mml:mo>)</mml:mo>
                              </mml:mrow>
                              <mml:mo>|</mml:mo>
                            </mml:mrow>
                            <mml:mo>·</mml:mo>
                            <mml:msup>
                              <mml:mo>ln</mml:mo>
                              <mml:mfrac>
                                <mml:mn>1</mml:mn>
                                <mml:mn>2</mml:mn>
                              </mml:mfrac>
                            </mml:msup>
                            <mml:mrow>
                              <mml:mo>(</mml:mo>
                            </mml:mrow>
                            <mml:mrow>
                              <mml:mo>|</mml:mo>
                              <mml:mi>f</mml:mi>
                              <mml:mrow>
                                <mml:mo>(</mml:mo>
                                <mml:mi>x</mml:mi>
                                <mml:mo>,</mml:mo>
                                <mml:mi>t</mml:mi>
                                <mml:mo>)</mml:mo>
                              </mml:mrow>
                              <mml:mo>|</mml:mo>
                            </mml:mrow>
                            <mml:mo>+</mml:mo>
                            <mml:mn>1</mml:mn>
                            <mml:mrow>
                              <mml:mo>)</mml:mo>
                            </mml:mrow>
                            <mml:mi>d</mml:mi>
                            <mml:mi>x</mml:mi>
                            <mml:msup>
                              <mml:mrow>
                                <mml:mo>}</mml:mo>
                              </mml:mrow>
                              <mml:mn>2</mml:mn>
                            </mml:msup>
                            <mml:mi>d</mml:mi>
                            <mml:mi>t</mml:mi>
                            <mml:mo>&lt;</mml:mo>
                            <mml:mi>∞</mml:mi>
                            <mml:mo>,</mml:mo>
                          </mml:mrow>
                        </mml:mtd>
                      </mml:mtr>
                    </mml:mtable>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:disp-formula>then for all divergence-free <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$u_0\in L^2(\Omega ;{\mathbb {R}}^2)$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:msub>
                      <mml:mi>u</mml:mi>
                      <mml:mn>0</mml:mn>
                    </mml:msub>
                    <mml:mo>∈</mml:mo>
                    <mml:msup>
                      <mml:mi>L</mml:mi>
                      <mml:mn>2</mml:mn>
                    </mml:msup>
                    <mml:mrow>
                      <mml:mo>(</mml:mo>
                      <mml:mi>Ω</mml:mi>
                      <mml:mo>;</mml:mo>
                      <mml:msup>
                        <mml:mrow>
                          <mml:mi>R</mml:mi>
                        </mml:mrow>
                        <mml:mn>2</mml:mn>
                      </mml:msup>
                      <mml:mo>)</mml:mo>
                    </mml:mrow>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>, a corresponding initial-boundary value problem admits a weak solution <jats:italic>u</jats:italic> with <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$u|_{t=0}=u_0$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:msub>
                      <mml:mrow>
                        <mml:mi>u</mml:mi>
                        <mml:mo>|</mml:mo>
                      </mml:mrow>
                      <mml:mrow>
                        <mml:mi>t</mml:mi>
                        <mml:mo>=</mml:mo>
                        <mml:mn>0</mml:mn>
                      </mml:mrow>
                    </mml:msub>
                    <mml:mo>=</mml:mo>
                    <mml:msub>
                      <mml:mi>u</mml:mi>
                      <mml:mn>0</mml:mn>
                    </mml:msub>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>. For any positive and nondecreasing <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$L\in C^0([0,\infty ))$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>L</mml:mi>
                    <mml:mo>∈</mml:mo>
                    <mml:msup>
                      <mml:mi>C</mml:mi>
                      <mml:mn>0</mml:mn>
                    </mml:msup>
                    <mml:mrow>
                      <mml:mo>(</mml:mo>
                      <mml:mrow>
                        <mml:mo>[</mml:mo>
                        <mml:mn>0</mml:mn>
                        <mml:mo>,</mml:mo>
                        <mml:mi>∞</mml:mi>
                        <mml:mo>)</mml:mo>
                      </mml:mrow>
                      <mml:mo>)</mml:mo>
                    </mml:mrow>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> such that <jats:disp-formula>
              <jats:alternatives>
                <jats:tex-math>$$\begin{aligned} \frac{L(\xi )}{\ln ^\frac{1}{2} \xi } \rightarrow 0 \qquad \text{ as } \xi \rightarrow \infty , \end{aligned}$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mtable>
                      <mml:mtr>
                        <mml:mtd>
                          <mml:mrow>
                            <mml:mfrac>
                              <mml:mrow>
                                <mml:mi>L</mml:mi>
                                <mml:mo>(</mml:mo>
                                <mml:mi>ξ</mml:mi>
                                <mml:mo>)</mml:mo>
                              </mml:mrow>
                              <mml:mrow>
                                <mml:msup>
                                  <mml:mo>ln</mml:mo>
                                  <mml:mfrac>
                                    <mml:mn>1</mml:mn>
                                    <mml:mn>2</mml:mn>
                                  </mml:mfrac>
                                </mml:msup>
                                <mml:mi>ξ</mml:mi>
                              </mml:mrow>
                            </mml:mfrac>
                            <mml:mo>→</mml:mo>
                            <mml:mn>0</mml:mn>
                            <mml:mspace/>
                            <mml:mspace/>
                            <mml:mtext>as</mml:mtext>
                            <mml:mspace/>
                            <mml:mi>ξ</mml:mi>
                            <mml:mo>→</mml:mo>
                            <mml:mi>∞</mml:mi>
                            <mml:mo>,</mml:mo>
                          </mml:mrow>
                        </mml:mtd>
                      </mml:mtr>
                    </mml:mtable>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:disp-formula>this is complemented by a statement on nonexistence of such a solution in the presence of smooth initial data and a suitably constructed <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$f:\Omega \times (0,T)\rightarrow {\mathbb {R}}^2$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>f</mml:mi>
                    <mml:mo>:</mml:mo>
                    <mml:mi>Ω</mml:mi>
                    <mml:mo>×</mml:mo>
                    <mml:mrow>
                      <mml:mo>(</mml:mo>
                      <mml:mn>0</mml:mn>
                      <mml:mo>,</mml:mo>
                      <mml:mi>T</mml:mi>
                      <mml:mo>)</mml:mo>
                    </mml:mrow>
                    <mml:mo>→</mml:mo>
                    <mml:msup>
                      <mml:mrow>
                        <mml:mi>R</mml:mi>
                      </mml:mrow>
                      <mml:mn>2</mml:mn>
                    </mml:msup>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> fulfilling <jats:disp-formula>
              <jats:alternatives>
                <jats:tex-math>$$\begin{aligned} \int _0^T \bigg \{ \int _\Omega |f(x,t)| \cdot L\big (|f(x,t)|\big ) dx \bigg \}^2 dt &lt; \infty . \end{aligned}$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mtable>
                      <mml:mtr>
                        <mml:mtd>
                          <mml:mrow>
                            <mml:msubsup>
                              <mml:mo>∫</mml:mo>
                              <mml:mn>0</mml:mn>
                              <mml:mi>T</mml:mi>
                            </mml:msubsup>
                            <mml:mrow>
                              <mml:mo>{</mml:mo>
                            </mml:mrow>
                            <mml:msub>
                              <mml:mo>∫</mml:mo>
                              <mml:mi>Ω</mml:mi>
                            </mml:msub>
                            <mml:mrow>
                              <mml:mo>|</mml:mo>
                              <mml:mi>f</mml:mi>
                              <mml:mrow>
                                <mml:mo>(</mml:mo>
                                <mml:mi>x</mml:mi>
                                <mml:mo>,</mml:mo>
                                <mml:mi>t</mml:mi>
                                <mml:mo>)</mml:mo>
                              </mml:mrow>
                              <mml:mo>|</mml:mo>
                            </mml:mrow>
                            <mml:mo>·</mml:mo>
                            <mml:mrow>
                              <mml:mi>L</mml:mi>
                              <mml:mrow>
                                <mml:mo>(</mml:mo>
                              </mml:mrow>
                              <mml:mo>|</mml:mo>
                              <mml:mi>f</mml:mi>
                              <mml:mrow>
                                <mml:mo>(</mml:mo>
                                <mml:mi>x</mml:mi>
                                <mml:mo>,</mml:mo>
                                <mml:mi>t</mml:mi>
                                <mml:mo>)</mml:mo>
                              </mml:mrow>
                              <mml:mo>|</mml:mo>
                              <mml:mrow>
                                <mml:mo>)</mml:mo>
                              </mml:mrow>
                              <mml:mi>d</mml:mi>
                              <mml:mi>x</mml:mi>
                            </mml:mrow>
                            <mml:msup>
                              <mml:mrow>
                                <mml:mo>}</mml:mo>
                              </mml:mrow>
                              <mml:mn>2</mml:mn>
                            </mml:msup>
                            <mml:mi>d</mml:mi>
                            <mml:mi>t</mml:mi>
                            <mml:mo>&lt;</mml:mo>
                            <mml:mi>∞</mml:mi>
                            <mml:mo>.</mml:mo>
                          </mml:mrow>
                        </mml:mtd>
                      </mml:mtr>
                    </mml:mtable>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:disp-formula>This resolves a fine structure in the borderline case <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$p=1$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>p</mml:mi>
                    <mml:mo>=</mml:mo>
                    <mml:mn>1</mml:mn>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> and <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$q=2$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>q</mml:mi>
                    <mml:mo>=</mml:mo>
                    <mml:mn>2</mml:mn>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> appearing in results on existence of weak solutions for sources in <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$L^q((0,T);L^p(\Omega ;{\mathbb {R}}^2))$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:msup>
                      <mml:mi>L</mml:mi>
                      <mml:mi>q</mml:mi>
                    </mml:msup>
                    <mml:mrow>
                      <mml:mo>(</mml:mo>
                      <mml:mrow>
                        <mml:mo>(</mml:mo>
                        <mml:mn>0</mml:mn>
                        <mml:mo>,</mml:mo>
                        <mml:mi>T</mml:mi>
                        <mml:mo>)</mml:mo>
                      </mml:mrow>
                      <mml:mo>;</mml:mo>
                      <mml:msup>
                        <mml:mi>L</mml:mi>
                        <mml:mi>p</mml:mi>
                      </mml:msup>
                      <mml:mrow>
                        <mml:mo>(</mml:mo>
                        <mml:mi>Ω</mml:mi>
                        <mml:mo>;</mml:mo>
                        <mml:msup>
                          <mml:mrow>
                            <mml:mi>R</mml:mi>
                          </mml:mrow>
                          <mml:mn>2</mml:mn>
                        </mml:msup>
                        <mml:mo>)</mml:mo>
                      </mml:mrow>
                      <mml:mo>)</mml:mo>
                    </mml:mrow>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> when <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$p\in (1,\infty ]$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>p</mml:mi>
                    <mml:mo>∈</mml:mo>
                    <mml:mo>(</mml:mo>
                    <mml:mn>1</mml:mn>
                    <mml:mo>,</mml:mo>
                    <mml:mi>∞</mml:mi>
                    <mml:mo>]</mml:mo>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> and <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$q\in [1,\infty ]$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>q</mml:mi>
                    <mml:mo>∈</mml:mo>
                    <mml:mo>[</mml:mo>
                    <mml:mn>1</mml:mn>
                    <mml:mo>,</mml:mo>
                    <mml:mi>∞</mml:mi>
                    <mml:mo>]</mml:mo>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> satisfy <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$\frac{1}{p}+\frac{1}{q}\le \frac{3}{2}$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mfrac>
                      <mml:mn>1</mml:mn>
                      <mml:mi>p</mml:mi>
                    </mml:mfrac>
                    <mml:mo>+</mml:mo>
                    <mml:mfrac>
                      <mml:mn>1</mml:mn>
                      <mml:mi>q</mml:mi>
                    </mml:mfrac>
                    <mml:mo>≤</mml:mo>
                    <mml:mfrac>
                      <mml:mn>3</mml:mn>
                      <mml:mn>2</mml:mn>
                    </mml:mfrac>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>, and on nonexistence if here <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$p\in [1,\infty )$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>p</mml:mi>
                    <mml:mo>∈</mml:mo>
                    <mml:mo>[</mml:mo>
                    <mml:mn>1</mml:mn>
                    <mml:mo>,</mml:mo>
                    <mml:mi>∞</mml:mi>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> and <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$q\in [1,\infty )$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>q</mml:mi>
                    <mml:mo>∈</mml:mo>
                    <mml:mo>[</mml:mo>
                    <mml:mn>1</mml:mn>
                    <mml:mo>,</mml:mo>
                    <mml:mi>∞</mml:mi>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> are such that <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$\frac{1}{p}+\frac{1}{q}&gt;\frac{3}{2}$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mfrac>
                      <mml:mn>1</mml:mn>
                      <mml:mi>p</mml:mi>
                    </mml:mfrac>
                    <mml:mo>+</mml:mo>
                    <mml:mfrac>
                      <mml:mn>1</mml:mn>
                      <mml:mi>q</mml:mi>
                    </mml:mfrac>
                    <mml:mo>&gt;</mml:mo>
                    <mml:mfrac>
                      <mml:mn>3</mml:mn>
                      <mml:mn>2</mml:mn>
                    </mml:mfrac>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>.</jats:p>}},
  author       = {{Winkler, Michael}},
  issn         = {{0025-5831}},
  journal      = {{Mathematische Annalen}},
  number       = {{2}},
  pages        = {{3023--3054}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Externally forced blow-up and optimal spaces for source regularity in the two-dimensional Navier–Stokes system}}},
  doi          = {{10.1007/s00208-024-02987-6}},
  volume       = {{391}},
  year         = {{2024}},
}

@article{63257,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>The quasilinear Keller–Segel system<jats:disp-formula><jats:alternatives><jats:tex-math>$$\begin{aligned} \left\{ \begin{array}{l} u_t=\nabla \cdot (D(u)\nabla u) - \nabla \cdot (S(u)\nabla v), \\ v_t=\Delta v-v+u, \end{array}\right. \end{aligned}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mfenced><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>∇</mml:mi><mml:mo>·</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>∇</mml:mi><mml:mi>u</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>-</mml:mo><mml:mi>∇</mml:mi><mml:mo>·</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>∇</mml:mi><mml:mi>v</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:msub><mml:mi>v</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>Δ</mml:mi><mml:mi>v</mml:mi><mml:mo>-</mml:mo><mml:mi>v</mml:mi><mml:mo>+</mml:mo><mml:mi>u</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mfenced></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></jats:alternatives></jats:disp-formula>endowed with homogeneous Neumann boundary conditions is considered in a bounded domain<jats:inline-formula><jats:alternatives><jats:tex-math>$$\Omega \subset {\mathbb {R}}^n$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Ω</mml:mi><mml:mo>⊂</mml:mo><mml:msup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>,<jats:inline-formula><jats:alternatives><jats:tex-math>$$n \ge 3$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>, with smooth boundary for sufficiently regular functions<jats:italic>D</jats:italic>and<jats:italic>S</jats:italic>satisfying<jats:inline-formula><jats:alternatives><jats:tex-math>$$D&gt;0$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>D</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>on<jats:inline-formula><jats:alternatives><jats:tex-math>$$[0,\infty )$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>∞</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>,<jats:inline-formula><jats:alternatives><jats:tex-math>$$S&gt;0$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>on<jats:inline-formula><jats:alternatives><jats:tex-math>$$(0,\infty )$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>∞</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>and<jats:inline-formula><jats:alternatives><jats:tex-math>$$S(0)=0$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>. On the one hand, it is shown that if<jats:inline-formula><jats:alternatives><jats:tex-math>$$\frac{S}{D}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:mi>S</mml:mi><mml:mi>D</mml:mi></mml:mfrac></mml:math></jats:alternatives></jats:inline-formula>satisfies the subcritical growth condition<jats:disp-formula><jats:alternatives><jats:tex-math>$$\begin{aligned} \frac{S(s)}{D(s)} \le C s^\alpha \qquad \text{ for } \text{ all } s\ge 1 \qquad \text{ with } \text{ some } \alpha &lt; \frac{2}{n} \end{aligned}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mfrac><mml:mrow><mml:mi>S</mml:mi><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mi>D</mml:mi><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac><mml:mo>≤</mml:mo><mml:mi>C</mml:mi><mml:msup><mml:mi>s</mml:mi><mml:mi>α</mml:mi></mml:msup><mml:mspace/><mml:mspace/><mml:mtext>for</mml:mtext><mml:mspace/><mml:mspace/><mml:mtext>all</mml:mtext><mml:mspace/><mml:mi>s</mml:mi><mml:mo>≥</mml:mo><mml:mn>1</mml:mn><mml:mspace/><mml:mspace/><mml:mtext>with</mml:mtext><mml:mspace/><mml:mspace/><mml:mtext>some</mml:mtext><mml:mspace/><mml:mi>α</mml:mi><mml:mo>&lt;</mml:mo><mml:mfrac><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mfrac></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></jats:alternatives></jats:disp-formula>and<jats:inline-formula><jats:alternatives><jats:tex-math>$$C&gt;0$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>C</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>, then for any sufficiently regular initial data there exists a global weak energy solution such that<jats:inline-formula><jats:alternatives><jats:tex-math>$${ \mathrm{{ess}}} \sup _{t&gt;0} \Vert u(t) \Vert _{L^p(\Omega )}&lt;\infty $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ess</mml:mi><mml:msub><mml:mo>sup</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mo>‖</mml:mo><mml:mi>u</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>‖</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>Ω</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>&lt;</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>for some<jats:inline-formula><jats:alternatives><jats:tex-math>$$p &gt; \frac{2n}{n+2}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&gt;</mml:mo><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>. On the other hand, if<jats:inline-formula><jats:alternatives><jats:tex-math>$$\frac{S}{D}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:mi>S</mml:mi><mml:mi>D</mml:mi></mml:mfrac></mml:math></jats:alternatives></jats:inline-formula>satisfies the supercritical growth condition<jats:disp-formula><jats:alternatives><jats:tex-math>$$\begin{aligned} \frac{S(s)}{D(s)} \ge c s^\alpha \qquad \text{ for } \text{ all } s\ge 1 \qquad \text{ with } \text{ some } \alpha &gt; \frac{2}{n} \end{aligned}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mfrac><mml:mrow><mml:mi>S</mml:mi><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mi>D</mml:mi><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac><mml:mo>≥</mml:mo><mml:mi>c</mml:mi><mml:msup><mml:mi>s</mml:mi><mml:mi>α</mml:mi></mml:msup><mml:mspace/><mml:mspace/><mml:mtext>for</mml:mtext><mml:mspace/><mml:mspace/><mml:mtext>all</mml:mtext><mml:mspace/><mml:mi>s</mml:mi><mml:mo>≥</mml:mo><mml:mn>1</mml:mn><mml:mspace/><mml:mspace/><mml:mtext>with</mml:mtext><mml:mspace/><mml:mspace/><mml:mtext>some</mml:mtext><mml:mspace/><mml:mi>α</mml:mi><mml:mo>&gt;</mml:mo><mml:mfrac><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mfrac></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></jats:alternatives></jats:disp-formula>and<jats:inline-formula><jats:alternatives><jats:tex-math>$$c&gt;0$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>c</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>, then the nonexistence of a global weak energy solution having the boundedness property stated above is shown for some initial data in the radial setting. This establishes some criticality of the value<jats:inline-formula><jats:alternatives><jats:tex-math>$$\alpha = \frac{2}{n}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mfrac></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>for<jats:inline-formula><jats:alternatives><jats:tex-math>$$n \ge 3$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>, without any additional assumption on the behavior of<jats:italic>D</jats:italic>(<jats:italic>s</jats:italic>) as<jats:inline-formula><jats:alternatives><jats:tex-math>$$s \rightarrow \infty $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>s</mml:mi><mml:mo>→</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>, in particular without requiring any algebraic lower bound for<jats:italic>D</jats:italic>. When applied to the Keller–Segel system with volume-filling effect for probability distribution functions of the type<jats:inline-formula><jats:alternatives><jats:tex-math>$$Q(s) = \exp (-s^\beta )$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Q</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>exp</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mo>-</mml:mo><mml:msup><mml:mi>s</mml:mi><mml:mi>β</mml:mi></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>,<jats:inline-formula><jats:alternatives><jats:tex-math>$$s \ge 0$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>s</mml:mi><mml:mo>≥</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>, for global solvability the exponent<jats:inline-formula><jats:alternatives><jats:tex-math>$$\beta = \frac{n-2}{n}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>β</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:mfrac></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>is seen to be critical.</jats:p>}},
  author       = {{Stinner, Christian and Winkler, Michael}},
  issn         = {{1424-3199}},
  journal      = {{Journal of Evolution Equations}},
  number       = {{2}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects}}},
  doi          = {{10.1007/s00028-024-00954-x}},
  volume       = {{24}},
  year         = {{2024}},
}

@article{63253,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>The Neumann problem for the Keller-Segel system <jats:inline-formula>
                     <jats:tex-math/>
                     <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                        <mml:mrow>
                           <mml:mtable columnalign="left" displaystyle="true">
                              <mml:mtr>
                                 <mml:mtd>
                                    <mml:mrow>
                                       <mml:mo>{</mml:mo>
                                       <mml:mtable columnalign="left" displaystyle="true">
                                          <mml:mtr>
                                             <mml:mtd>
                                                <mml:msub>
                                                   <mml:mi>u</mml:mi>
                                                   <mml:mi>t</mml:mi>
                                                </mml:msub>
                                                <mml:mo>=</mml:mo>
                                                <mml:mi mathvariant="normal">∇</mml:mi>
                                                <mml:mo>⋅</mml:mo>
                                                <mml:mrow>
                                                   <mml:mo>(</mml:mo>
                                                   <mml:mi>D</mml:mi>
                                                   <mml:mrow>
                                                      <mml:mo>(</mml:mo>
                                                      <mml:mi>u</mml:mi>
                                                      <mml:mo>)</mml:mo>
                                                   </mml:mrow>
                                                   <mml:mi mathvariant="normal">∇</mml:mi>
                                                   <mml:mi>u</mml:mi>
                                                   <mml:mo>)</mml:mo>
                                                </mml:mrow>
                                                <mml:mo>−</mml:mo>
                                                <mml:mi mathvariant="normal">∇</mml:mi>
                                                <mml:mo>⋅</mml:mo>
                                                <mml:mrow>
                                                   <mml:mo>(</mml:mo>
                                                   <mml:mi>S</mml:mi>
                                                   <mml:mrow>
                                                      <mml:mo>(</mml:mo>
                                                      <mml:mi>u</mml:mi>
                                                      <mml:mo>)</mml:mo>
                                                   </mml:mrow>
                                                   <mml:mi mathvariant="normal">∇</mml:mi>
                                                   <mml:mi>v</mml:mi>
                                                   <mml:mo>)</mml:mo>
                                                </mml:mrow>
                                                <mml:mo>,</mml:mo>
                                             </mml:mtd>
                                          </mml:mtr>
                                          <mml:mtr>
                                             <mml:mtd>
                                                <mml:mn>0</mml:mn>
                                                <mml:mo>=</mml:mo>
                                                <mml:mi mathvariant="normal">Δ</mml:mi>
                                                <mml:mi>v</mml:mi>
                                                <mml:mo>−</mml:mo>
                                                <mml:mi>μ</mml:mi>
                                                <mml:mo>+</mml:mo>
                                                <mml:mi>u</mml:mi>
                                                <mml:mo>,</mml:mo>
                                                <mml:mstyle scriptlevel="0"/>
                                                <mml:mi>μ</mml:mi>
                                                <mml:mo>=</mml:mo>
                                                <mml:mstyle displaystyle="true" scriptlevel="0">
                                                   <mml:mo>−</mml:mo>
                                                   <mml:mstyle scriptlevel="0"/>
                                                   <mml:mstyle scriptlevel="0"/>
                                                   <mml:mstyle scriptlevel="0"/>
                                                   <mml:mstyle scriptlevel="0"/>
                                                   <mml:mstyle scriptlevel="0"/>
                                                   <mml:mstyle scriptlevel="0"/>
                                                   <mml:mstyle scriptlevel="0"/>
                                                   <mml:mstyle scriptlevel="0"/>
                                                   <mml:mstyle scriptlevel="0"/>
                                                   <mml:msub>
                                                      <mml:mo>∫</mml:mo>
                                                      <mml:mi mathvariant="normal">Ω</mml:mi>
                                                   </mml:msub>
                                                   <mml:mi>u</mml:mi>
                                                   <mml:mtext>d</mml:mtext>
                                                   <mml:mi>x</mml:mi>
                                                   <mml:mo>,</mml:mo>
                                                </mml:mstyle>
                                             </mml:mtd>
                                          </mml:mtr>
                                       </mml:mtable>
                                    </mml:mrow>
                                 </mml:mtd>
                              </mml:mtr>
                           </mml:mtable>
                        </mml:mrow>
                     </mml:math>
                  </jats:inline-formula> is considered in <jats:italic>n</jats:italic>-dimensional balls Ω with <jats:inline-formula>
                     <jats:tex-math/>
                     <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                        <mml:mrow>
                           <mml:mi>n</mml:mi>
                           <mml:mtext>⩾</mml:mtext>
                           <mml:mn>2</mml:mn>
                        </mml:mrow>
                     </mml:math>
                  </jats:inline-formula>, with suitably regular and radially symmetric, radially nonincreasing initial data <jats:italic>u</jats:italic>
                  <jats:sub>0</jats:sub>. The functions <jats:italic>D</jats:italic> and <jats:italic>S</jats:italic> are only assumed to belong to <jats:inline-formula>
                     <jats:tex-math/>
                     <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                        <mml:mrow>
                           <mml:msup>
                              <mml:mi>C</mml:mi>
                              <mml:mn>2</mml:mn>
                           </mml:msup>
                           <mml:mo stretchy="false">(</mml:mo>
                           <mml:mo stretchy="false">[</mml:mo>
                           <mml:mn>0</mml:mn>
                           <mml:mo>,</mml:mo>
                           <mml:mi mathvariant="normal">∞</mml:mi>
                           <mml:mo stretchy="false">)</mml:mo>
                           <mml:mo stretchy="false">)</mml:mo>
                        </mml:mrow>
                     </mml:math>
                  </jats:inline-formula> and to satisfy <jats:italic>D</jats:italic> &gt; 0 and <jats:inline-formula>
                     <jats:tex-math/>
                     <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                        <mml:mrow>
                           <mml:mi>S</mml:mi>
                           <mml:mtext>⩾</mml:mtext>
                           <mml:mn>0</mml:mn>
                        </mml:mrow>
                     </mml:math>
                  </jats:inline-formula> on <jats:inline-formula>
                     <jats:tex-math/>
                     <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                        <mml:mrow>
                           <mml:mo stretchy="false">[</mml:mo>
                           <mml:mn>0</mml:mn>
                           <mml:mo>,</mml:mo>
                           <mml:mi mathvariant="normal">∞</mml:mi>
                           <mml:mo stretchy="false">)</mml:mo>
                        </mml:mrow>
                     </mml:math>
                  </jats:inline-formula> as well as <jats:inline-formula>
                     <jats:tex-math/>
                     <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                        <mml:mrow>
                           <mml:mi>S</mml:mi>
                           <mml:mo stretchy="false">(</mml:mo>
                           <mml:mn>0</mml:mn>
                           <mml:mo stretchy="false">)</mml:mo>
                           <mml:mo>=</mml:mo>
                           <mml:mn>0</mml:mn>
                        </mml:mrow>
                     </mml:math>
                  </jats:inline-formula>; in particular, diffusivities with arbitrarily fast decay are included.</jats:p>
               <jats:p>In this general context, it is shown that it is merely the asymptotic behavior as <jats:inline-formula>
                     <jats:tex-math/>
                     <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                        <mml:mrow>
                           <mml:mi>ξ</mml:mi>
                           <mml:mo accent="false" stretchy="false">→</mml:mo>
                           <mml:mi mathvariant="normal">∞</mml:mi>
                        </mml:mrow>
                     </mml:math>
                  </jats:inline-formula> of the expression <jats:inline-formula>
                     <jats:tex-math/>
                     <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                        <mml:mrow>
                           <mml:mtable columnalign="left" displaystyle="true">
                              <mml:mtr>
                                 <mml:mtd>
                                    <mml:mi>I</mml:mi>
                                    <mml:mrow>
                                       <mml:mo>(</mml:mo>
                                       <mml:mi>ξ</mml:mi>
                                       <mml:mo>)</mml:mo>
                                    </mml:mrow>
                                    <mml:mo>:=</mml:mo>
                                    <mml:mfrac>
                                       <mml:mrow>
                                          <mml:mi>S</mml:mi>
                                          <mml:mrow>
                                             <mml:mo>(</mml:mo>
                                             <mml:mi>ξ</mml:mi>
                                             <mml:mo>)</mml:mo>
                                          </mml:mrow>
                                       </mml:mrow>
                                       <mml:mrow>
                                          <mml:msup>
                                             <mml:mi>ξ</mml:mi>
                                             <mml:mfrac>
                                                <mml:mn>2</mml:mn>
                                                <mml:mi>n</mml:mi>
                                             </mml:mfrac>
                                          </mml:msup>
                                          <mml:mi>D</mml:mi>
                                          <mml:mrow>
                                             <mml:mo>(</mml:mo>
                                             <mml:mi>ξ</mml:mi>
                                             <mml:mo>)</mml:mo>
                                          </mml:mrow>
                                       </mml:mrow>
                                    </mml:mfrac>
                                    <mml:mo>,</mml:mo>
                                    <mml:mstyle scriptlevel="0"/>
                                    <mml:mi>ξ</mml:mi>
                                    <mml:mo>&gt;</mml:mo>
                                    <mml:mn>0</mml:mn>
                                    <mml:mo>,</mml:mo>
                                 </mml:mtd>
                              </mml:mtr>
                           </mml:mtable>
                        </mml:mrow>
                     </mml:math>
                  </jats:inline-formula> which decides about the occurrence of blow-up: Namely, it is seen that
<jats:list id="nonad871al1" list-type="bullet">
                     <jats:list-item id="nonad871al1.1">
                        <jats:label>•</jats:label>
                        <jats:p>if <jats:inline-formula>
                              <jats:tex-math/>
                              <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                                 <mml:mrow>
                                    <mml:munder>
                                       <mml:mo movablelimits="true">lim</mml:mo>
                                       <mml:mrow>
                                          <mml:mi>ξ</mml:mi>
                                          <mml:mo accent="false" stretchy="false">→</mml:mo>
                                          <mml:mi mathvariant="normal">∞</mml:mi>
                                       </mml:mrow>
                                    </mml:munder>
                                    <mml:mi>I</mml:mi>
                                    <mml:mo stretchy="false">(</mml:mo>
                                    <mml:mi>ξ</mml:mi>
                                    <mml:mo stretchy="false">)</mml:mo>
                                    <mml:mo>=</mml:mo>
                                    <mml:mn>0</mml:mn>
                                 </mml:mrow>
                              </mml:math>
                           </jats:inline-formula>, then any such solution is global and bounded, that</jats:p>
                     </jats:list-item>
                     <jats:list-item id="nonad871al1.2">
                        <jats:label>•</jats:label>
                        <jats:p>if <jats:inline-formula>
                              <jats:tex-math/>
                              <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                                 <mml:mrow>
                                    <mml:munder>
                                       <mml:mo movablelimits="true">lim sup</mml:mo>
                                       <mml:mrow>
                                          <mml:mi>ξ</mml:mi>
                                          <mml:mo accent="false" stretchy="false">→</mml:mo>
                                          <mml:mi mathvariant="normal">∞</mml:mi>
                                       </mml:mrow>
                                    </mml:munder>
                                    <mml:mi>I</mml:mi>
                                    <mml:mo stretchy="false">(</mml:mo>
                                    <mml:mi>ξ</mml:mi>
                                    <mml:mo stretchy="false">)</mml:mo>
                                    <mml:mo>&lt;</mml:mo>
                                    <mml:mi mathvariant="normal">∞</mml:mi>
                                 </mml:mrow>
                              </mml:math>
                           </jats:inline-formula> and <jats:inline-formula>
                              <jats:tex-math/>
                              <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                                 <mml:mrow>
                                    <mml:msub>
                                       <mml:mo>∫</mml:mo>
                                       <mml:mi mathvariant="normal">Ω</mml:mi>
                                    </mml:msub>
                                    <mml:msub>
                                       <mml:mi>u</mml:mi>
                                       <mml:mn>0</mml:mn>
                                    </mml:msub>
                                 </mml:mrow>
                              </mml:math>
                           </jats:inline-formula> is suitably small, then the corresponding solution is global and bounded, and that</jats:p>
                     </jats:list-item>
                     <jats:list-item id="nonad871al1.3">
                        <jats:label>•</jats:label>
                        <jats:p>if <jats:inline-formula>
                              <jats:tex-math/>
                              <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                                 <mml:mrow>
                                    <mml:munder>
                                       <mml:mo movablelimits="true">lim inf</mml:mo>
                                       <mml:mrow>
                                          <mml:mi>ξ</mml:mi>
                                          <mml:mo accent="false" stretchy="false">→</mml:mo>
                                          <mml:mi mathvariant="normal">∞</mml:mi>
                                       </mml:mrow>
                                    </mml:munder>
                                    <mml:mi>I</mml:mi>
                                    <mml:mo stretchy="false">(</mml:mo>
                                    <mml:mi>ξ</mml:mi>
                                    <mml:mo stretchy="false">)</mml:mo>
                                    <mml:mo>&gt;</mml:mo>
                                    <mml:mn>0</mml:mn>
                                 </mml:mrow>
                              </mml:math>
                           </jats:inline-formula>, then at each appropriately large mass level <jats:italic>m</jats:italic>, there exist radial initial data <jats:italic>u</jats:italic>
                           <jats:sub>0</jats:sub> such that <jats:inline-formula>
                              <jats:tex-math/>
                              <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                                 <mml:mrow>
                                    <mml:msub>
                                       <mml:mo>∫</mml:mo>
                                       <mml:mi mathvariant="normal">Ω</mml:mi>
                                    </mml:msub>
                                    <mml:msub>
                                       <mml:mi>u</mml:mi>
                                       <mml:mn>0</mml:mn>
                                    </mml:msub>
                                    <mml:mo>=</mml:mo>
                                    <mml:mi>m</mml:mi>
                                 </mml:mrow>
                              </mml:math>
                           </jats:inline-formula>, and that the associated solution blows up either in finite or in infinite time.</jats:p>
                     </jats:list-item>
                  </jats:list>
               </jats:p>
               <jats:p>This especially reveals the presence of critical mass phenomena whenever <jats:inline-formula>
                     <jats:tex-math/>
                     <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                        <mml:mrow>
                           <mml:munder>
                              <mml:mo movablelimits="true">lim</mml:mo>
                              <mml:mrow>
                                 <mml:mi>ξ</mml:mi>
                                 <mml:mo accent="false" stretchy="false">→</mml:mo>
                                 <mml:mi mathvariant="normal">∞</mml:mi>
                              </mml:mrow>
                           </mml:munder>
                           <mml:mi>I</mml:mi>
                           <mml:mo stretchy="false">(</mml:mo>
                           <mml:mi>ξ</mml:mi>
                           <mml:mo stretchy="false">)</mml:mo>
                           <mml:mo>∈</mml:mo>
                           <mml:mo stretchy="false">(</mml:mo>
                           <mml:mn>0</mml:mn>
                           <mml:mo>,</mml:mo>
                           <mml:mi mathvariant="normal">∞</mml:mi>
                           <mml:mo stretchy="false">)</mml:mo>
                        </mml:mrow>
                     </mml:math>
                  </jats:inline-formula> exists.</jats:p>}},
  author       = {{Ding, Mengyao and Winkler, Michael}},
  issn         = {{0951-7715}},
  journal      = {{Nonlinearity}},
  number       = {{12}},
  publisher    = {{IOP Publishing}},
  title        = {{{Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture}}},
  doi          = {{10.1088/1361-6544/ad871a}},
  volume       = {{37}},
  year         = {{2024}},
}

@article{63254,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>The chemotaxis-Navier–Stokes system <jats:disp-formula><jats:alternatives><jats:tex-math>$$\begin{aligned} \left\{ \begin{array}{rcl} n_t+u\cdot \nabla n &amp; =&amp;  \Delta \big (n c^{-\alpha } \big ), \\ c_t+ u\cdot \nabla c &amp; =&amp;  \Delta c -nc,\\ u_t + (u\cdot \nabla ) u &amp; =&amp; \Delta u+\nabla P + n\nabla \Phi , \qquad \nabla \cdot u=0, \end{array} \right. \end{aligned}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mtable>
                      <mml:mtr>
                        <mml:mtd>
                          <mml:mfenced>
                            <mml:mrow>
                              <mml:mtable>
                                <mml:mtr>
                                  <mml:mtd>
                                    <mml:mrow>
                                      <mml:msub>
                                        <mml:mi>n</mml:mi>
                                        <mml:mi>t</mml:mi>
                                      </mml:msub>
                                      <mml:mo>+</mml:mo>
                                      <mml:mi>u</mml:mi>
                                      <mml:mo>·</mml:mo>
                                      <mml:mi>∇</mml:mi>
                                      <mml:mi>n</mml:mi>
                                    </mml:mrow>
                                  </mml:mtd>
                                  <mml:mtd>
                                    <mml:mo>=</mml:mo>
                                  </mml:mtd>
                                  <mml:mtd>
                                    <mml:mrow>
                                      <mml:mi>Δ</mml:mi>
                                      <mml:mrow>
                                        <mml:mo>(</mml:mo>
                                      </mml:mrow>
                                      <mml:mi>n</mml:mi>
                                      <mml:msup>
                                        <mml:mi>c</mml:mi>
                                        <mml:mrow>
                                          <mml:mo>-</mml:mo>
                                          <mml:mi>α</mml:mi>
                                        </mml:mrow>
                                      </mml:msup>
                                      <mml:mrow>
                                        <mml:mo>)</mml:mo>
                                      </mml:mrow>
                                      <mml:mo>,</mml:mo>
                                    </mml:mrow>
                                  </mml:mtd>
                                </mml:mtr>
                                <mml:mtr>
                                  <mml:mtd>
                                    <mml:mrow>
                                      <mml:mrow/>
                                      <mml:msub>
                                        <mml:mi>c</mml:mi>
                                        <mml:mi>t</mml:mi>
                                      </mml:msub>
                                      <mml:mo>+</mml:mo>
                                      <mml:mi>u</mml:mi>
                                      <mml:mo>·</mml:mo>
                                      <mml:mi>∇</mml:mi>
                                      <mml:mi>c</mml:mi>
                                    </mml:mrow>
                                  </mml:mtd>
                                  <mml:mtd>
                                    <mml:mo>=</mml:mo>
                                  </mml:mtd>
                                  <mml:mtd>
                                    <mml:mrow>
                                      <mml:mi>Δ</mml:mi>
                                      <mml:mi>c</mml:mi>
                                      <mml:mo>-</mml:mo>
                                      <mml:mi>n</mml:mi>
                                      <mml:mi>c</mml:mi>
                                      <mml:mo>,</mml:mo>
                                    </mml:mrow>
                                  </mml:mtd>
                                </mml:mtr>
                                <mml:mtr>
                                  <mml:mtd>
                                    <mml:mrow>
                                      <mml:mrow/>
                                      <mml:msub>
                                        <mml:mi>u</mml:mi>
                                        <mml:mi>t</mml:mi>
                                      </mml:msub>
                                      <mml:mo>+</mml:mo>
                                      <mml:mrow>
                                        <mml:mo>(</mml:mo>
                                        <mml:mi>u</mml:mi>
                                        <mml:mo>·</mml:mo>
                                        <mml:mi>∇</mml:mi>
                                        <mml:mo>)</mml:mo>
                                      </mml:mrow>
                                      <mml:mi>u</mml:mi>
                                    </mml:mrow>
                                  </mml:mtd>
                                  <mml:mtd>
                                    <mml:mo>=</mml:mo>
                                  </mml:mtd>
                                  <mml:mtd>
                                    <mml:mrow>
                                      <mml:mi>Δ</mml:mi>
                                      <mml:mi>u</mml:mi>
                                      <mml:mo>+</mml:mo>
                                      <mml:mi>∇</mml:mi>
                                      <mml:mi>P</mml:mi>
                                      <mml:mo>+</mml:mo>
                                      <mml:mi>n</mml:mi>
                                      <mml:mi>∇</mml:mi>
                                      <mml:mi>Φ</mml:mi>
                                      <mml:mo>,</mml:mo>
                                      <mml:mspace/>
                                      <mml:mi>∇</mml:mi>
                                      <mml:mo>·</mml:mo>
                                      <mml:mi>u</mml:mi>
                                      <mml:mo>=</mml:mo>
                                      <mml:mn>0</mml:mn>
                                      <mml:mo>,</mml:mo>
                                    </mml:mrow>
                                  </mml:mtd>
                                </mml:mtr>
                              </mml:mtable>
                            </mml:mrow>
                          </mml:mfenced>
                        </mml:mtd>
                      </mml:mtr>
                    </mml:mtable>
                  </mml:mrow>
                </mml:math></jats:alternatives></jats:disp-formula>modelling the behavior of aerobic bacteria in a fluid drop, is considered in a smoothly bounded domain <jats:inline-formula><jats:alternatives><jats:tex-math>$$\Omega \subset \mathbb R^2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>Ω</mml:mi>
                    <mml:mo>⊂</mml:mo>
                    <mml:msup>
                      <mml:mi>R</mml:mi>
                      <mml:mn>2</mml:mn>
                    </mml:msup>
                  </mml:mrow>
                </mml:math></jats:alternatives></jats:inline-formula>. For all <jats:inline-formula><jats:alternatives><jats:tex-math>$$\alpha &gt; 0$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>α</mml:mi>
                    <mml:mo>&gt;</mml:mo>
                    <mml:mn>0</mml:mn>
                  </mml:mrow>
                </mml:math></jats:alternatives></jats:inline-formula> and all sufficiently regular <jats:inline-formula><jats:alternatives><jats:tex-math>$$\Phi $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mi>Φ</mml:mi>
                </mml:math></jats:alternatives></jats:inline-formula>, we construct global classical solutions and thereby extend recent results for the fluid-free analogue to the system coupled to a Navier–Stokes system. As a crucial new challenge, our analysis requires a priori estimates for <jats:italic>u</jats:italic> at a point in the proof when knowledge about <jats:italic>n</jats:italic> is essentially limited to the observation that the mass is conserved. To overcome this problem, we also prove new uniform-in-time <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^p$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:msup>
                    <mml:mi>L</mml:mi>
                    <mml:mi>p</mml:mi>
                  </mml:msup>
                </mml:math></jats:alternatives></jats:inline-formula> estimates for solutions to the inhomogeneous Navier–Stokes equations merely depending on the space-time <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:msup>
                    <mml:mi>L</mml:mi>
                    <mml:mn>2</mml:mn>
                  </mml:msup>
                </mml:math></jats:alternatives></jats:inline-formula> norm of the force term raised to an arbitrary small power.</jats:p>}},
  author       = {{Fuest, Mario and Winkler, Michael}},
  issn         = {{1422-6928}},
  journal      = {{Journal of Mathematical Fluid Mechanics}},
  number       = {{4}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing}}},
  doi          = {{10.1007/s00021-024-00899-8}},
  volume       = {{26}},
  year         = {{2024}},
}

@article{63262,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>Radially symmetric global unbounded solutions of the chemotaxis system <jats:disp-formula><jats:alternatives><jats:tex-math>$$\left\{ {\matrix{{{u_t} = \nabla \cdot (D(u)\nabla u) - \nabla \cdot (uS(u)\nabla v),} \hfill &amp; {} \hfill \cr {0 = \Delta v - \mu + u,} \hfill &amp; {\mu = {1 \over {|\Omega |}}\int_\Omega {u,} } \hfill \cr } } \right.$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mrow>
                      <mml:mo>{</mml:mo>
                      <mml:mrow>
                        <mml:mtable>
                          <mml:mtr>
                            <mml:mtd>
                              <mml:mrow>
                                <mml:msub>
                                  <mml:mi>u</mml:mi>
                                  <mml:mi>t</mml:mi>
                                </mml:msub>
                                <mml:mo>=</mml:mo>
                                <mml:mo>∇</mml:mo>
                                <mml:mo>⋅</mml:mo>
                                <mml:mo>(</mml:mo>
                                <mml:mi>D</mml:mi>
                                <mml:mo>(</mml:mo>
                                <mml:mi>u</mml:mi>
                                <mml:mo>)</mml:mo>
                                <mml:mo>∇</mml:mo>
                                <mml:mi>u</mml:mi>
                                <mml:mo>)</mml:mo>
                                <mml:mo>−</mml:mo>
                                <mml:mo>∇</mml:mo>
                                <mml:mo>⋅</mml:mo>
                                <mml:mo>(</mml:mo>
                                <mml:mi>u</mml:mi>
                                <mml:mi>S</mml:mi>
                                <mml:mo>(</mml:mo>
                                <mml:mi>u</mml:mi>
                                <mml:mo>)</mml:mo>
                                <mml:mo>∇</mml:mo>
                                <mml:mi>v</mml:mi>
                                <mml:mo>)</mml:mo>
                                <mml:mo>,</mml:mo>
                              </mml:mrow>
                            </mml:mtd>
                            <mml:mtd>
                              <mml:mrow/>
                            </mml:mtd>
                          </mml:mtr>
                          <mml:mtr>
                            <mml:mtd>
                              <mml:mrow>
                                <mml:mn>0</mml:mn>
                                <mml:mo>=</mml:mo>
                                <mml:mi>Δ</mml:mi>
                                <mml:mi>v</mml:mi>
                                <mml:mo>−</mml:mo>
                                <mml:mi>μ</mml:mi>
                                <mml:mo>+</mml:mo>
                                <mml:mi>u</mml:mi>
                                <mml:mo>,</mml:mo>
                              </mml:mrow>
                            </mml:mtd>
                            <mml:mtd>
                              <mml:mrow>
                                <mml:mi>μ</mml:mi>
                                <mml:mo>=</mml:mo>
                                <mml:mfrac>
                                  <mml:mn>1</mml:mn>
                                  <mml:mrow>
                                    <mml:mo>|</mml:mo>
                                    <mml:mi>Ω</mml:mi>
                                    <mml:mo>|</mml:mo>
                                  </mml:mrow>
                                </mml:mfrac>
                                <mml:mstyle>
                                  <mml:mrow>
                                    <mml:msub>
                                      <mml:mo>∫</mml:mo>
                                      <mml:mi>Ω</mml:mi>
                                    </mml:msub>
                                    <mml:mrow>
                                      <mml:mi>u</mml:mi>
                                      <mml:mo>,</mml:mo>
                                    </mml:mrow>
                                  </mml:mrow>
                                </mml:mstyle>
                              </mml:mrow>
                            </mml:mtd>
                          </mml:mtr>
                        </mml:mtable>
                      </mml:mrow>
                    </mml:mrow>
                  </mml:mrow>
                </mml:math></jats:alternatives></jats:disp-formula> are considered in a ball Ω = <jats:italic>B</jats:italic><jats:sub><jats:italic>R</jats:italic></jats:sub>(0) ⊂ ℝ<jats:sup><jats:italic>n</jats:italic></jats:sup>, where <jats:italic>n</jats:italic> ≥ 3 and <jats:italic>R</jats:italic> &gt; 0.</jats:p><jats:p>Under the assumption that <jats:italic>D</jats:italic> and <jats:italic>S</jats:italic> suitably generalize the prototypes given by <jats:italic>D</jats:italic>(<jats:italic>ξ</jats:italic>) = (<jats:italic>ξ</jats:italic> + <jats:italic>ι</jats:italic>)<jats:sup>m−1</jats:sup> and <jats:italic>S</jats:italic>(<jats:italic>ξ</jats:italic>) = (<jats:italic>ξ</jats:italic> + 1)<jats:sup>−λ−1</jats:sup> for all <jats:italic>ξ</jats:italic> &gt; 0 and some <jats:italic>m</jats:italic> ∈ ℝ, λ &gt;0 and <jats:italic>ι</jats:italic> ≥ 0 fulfilling <jats:inline-formula><jats:alternatives><jats:tex-math>$$m + \lambda &lt; 1 - {2 \over n}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mi>m</mml:mi>
                  <mml:mo>+</mml:mo>
                  <mml:mi>λ</mml:mi>
                  <mml:mo>&lt;</mml:mo>
                  <mml:mn>1</mml:mn>
                  <mml:mo>−</mml:mo>
                  <mml:mfrac>
                    <mml:mn>2</mml:mn>
                    <mml:mi>n</mml:mi>
                  </mml:mfrac>
                </mml:math></jats:alternatives></jats:inline-formula>, a considerably large set of initial data <jats:italic>u</jats:italic><jats:sub>0</jats:sub> is found to enforce a complete mass aggregation in infinite time in the sense that for any such <jats:italic>u</jats:italic><jats:sub>0</jats:sub>, an associated Neumann type initial-boundary value problem admits a global classical solution (<jats:italic>u, v</jats:italic>) satisfying <jats:disp-formula><jats:alternatives><jats:tex-math>$${1 \over C} \cdot {(t + 1)^{{1 \over \lambda }}} \le ||u( \cdot ,t)|{|_{{L^\infty }(\Omega )}} \le C \cdot {(t + 1)^{{1 \over \lambda }}}\,\,\,{\rm{for}}\,\,{\rm{all}}\,\,t &gt; 0$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mfrac>
                      <mml:mn>1</mml:mn>
                      <mml:mi>C</mml:mi>
                    </mml:mfrac>
                  </mml:mrow>
                  <mml:mo>⋅</mml:mo>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mi>t</mml:mi>
                    <mml:mo>+</mml:mo>
                    <mml:mn>1</mml:mn>
                    <mml:msup>
                      <mml:mo>)</mml:mo>
                      <mml:mrow>
                        <mml:mrow>
                          <mml:mfrac>
                            <mml:mn>1</mml:mn>
                            <mml:mi>λ</mml:mi>
                          </mml:mfrac>
                        </mml:mrow>
                      </mml:mrow>
                    </mml:msup>
                  </mml:mrow>
                  <mml:mo>≤</mml:mo>
                  <mml:mrow>
                    <mml:mo>|</mml:mo>
                  </mml:mrow>
                  <mml:mrow>
                    <mml:mo>|</mml:mo>
                  </mml:mrow>
                  <mml:mi>u</mml:mi>
                  <mml:mo>(</mml:mo>
                  <mml:mo>⋅</mml:mo>
                  <mml:mo>,</mml:mo>
                  <mml:mi>t</mml:mi>
                  <mml:mo>)</mml:mo>
                  <mml:mrow>
                    <mml:mo>|</mml:mo>
                  </mml:mrow>
                  <mml:mrow>
                    <mml:msub>
                      <mml:mrow>
                        <mml:mo>|</mml:mo>
                      </mml:mrow>
                      <mml:mrow>
                        <mml:mrow>
                          <mml:msup>
                            <mml:mi>L</mml:mi>
                            <mml:mi>∞</mml:mi>
                          </mml:msup>
                        </mml:mrow>
                        <mml:mo>(</mml:mo>
                        <mml:mi>Ω</mml:mi>
                        <mml:mo>)</mml:mo>
                      </mml:mrow>
                    </mml:msub>
                  </mml:mrow>
                  <mml:mo>≤</mml:mo>
                  <mml:mi>C</mml:mi>
                  <mml:mo>⋅</mml:mo>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mi>t</mml:mi>
                    <mml:mo>+</mml:mo>
                    <mml:mn>1</mml:mn>
                    <mml:msup>
                      <mml:mo>)</mml:mo>
                      <mml:mrow>
                        <mml:mrow>
                          <mml:mfrac>
                            <mml:mn>1</mml:mn>
                            <mml:mi>λ</mml:mi>
                          </mml:mfrac>
                        </mml:mrow>
                      </mml:mrow>
                    </mml:msup>
                  </mml:mrow>
                  <mml:mspace/>
                  <mml:mspace/>
                  <mml:mspace/>
                  <mml:mrow>
                    <mml:mrow>
                      <mml:mi>f</mml:mi>
                      <mml:mi>o</mml:mi>
                      <mml:mi>r</mml:mi>
                    </mml:mrow>
                  </mml:mrow>
                  <mml:mspace/>
                  <mml:mspace/>
                  <mml:mrow>
                    <mml:mrow>
                      <mml:mi>a</mml:mi>
                      <mml:mi>l</mml:mi>
                      <mml:mi>l</mml:mi>
                    </mml:mrow>
                  </mml:mrow>
                  <mml:mspace/>
                  <mml:mspace/>
                  <mml:mi>t</mml:mi>
                  <mml:mo>&gt;</mml:mo>
                  <mml:mn>0</mml:mn>
                </mml:math></jats:alternatives></jats:disp-formula> as well as <jats:disp-formula><jats:alternatives><jats:tex-math>$$||u( \cdot \,,t)|{|_{{L^1}(\Omega \backslash {B_{{r_0}}}(0))}} \to 0\,\,\,{\rm{as}}\,\,t \to \infty \,\,\,{\rm{for}}\,\,{\rm{all}}\,\,{r_0} \in (0,R)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mo>|</mml:mo>
                  <mml:mo>|</mml:mo>
                  <mml:mi>u</mml:mi>
                  <mml:mo>(</mml:mo>
                  <mml:mo>⋅</mml:mo>
                  <mml:mo>,</mml:mo>
                  <mml:mi>t</mml:mi>
                  <mml:mo>)</mml:mo>
                  <mml:mo>|</mml:mo>
                  <mml:msub>
                    <mml:mo>|</mml:mo>
                    <mml:mrow>
                      <mml:msup>
                        <mml:mi>L</mml:mi>
                        <mml:mn>1</mml:mn>
                      </mml:msup>
                      <mml:mo>(</mml:mo>
                      <mml:mi>Ω</mml:mi>
                      <mml:mo>\</mml:mo>
                      <mml:msub>
                        <mml:mi>B</mml:mi>
                        <mml:mrow>
                          <mml:msub>
                            <mml:mi>r</mml:mi>
                            <mml:mn>0</mml:mn>
                          </mml:msub>
                        </mml:mrow>
                      </mml:msub>
                      <mml:mo>(</mml:mo>
                      <mml:mn>0</mml:mn>
                      <mml:mo>)</mml:mo>
                      <mml:mo>)</mml:mo>
                    </mml:mrow>
                  </mml:msub>
                  <mml:mo>→</mml:mo>
                  <mml:mn>0</mml:mn>
                  <mml:mtext>as</mml:mtext>
                  <mml:mi>t</mml:mi>
                  <mml:mo>→</mml:mo>
                  <mml:mi>∞</mml:mi>
                  <mml:mtext>for all</mml:mtext>
                  <mml:msub>
                    <mml:mi>r</mml:mi>
                    <mml:mn>0</mml:mn>
                  </mml:msub>
                  <mml:mo>∈</mml:mo>
                  <mml:mo>(</mml:mo>
                  <mml:mn>0</mml:mn>
                  <mml:mo>,</mml:mo>
                  <mml:mi>R</mml:mi>
                  <mml:mo>)</mml:mo>
                </mml:math></jats:alternatives></jats:disp-formula> with some <jats:italic>C</jats:italic> &gt; 0.</jats:p>}},
  author       = {{Winkler, Michael}},
  issn         = {{0021-2172}},
  journal      = {{Israel Journal of Mathematics}},
  number       = {{1}},
  pages        = {{93--127}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Complete infinite-time mass aggregation in a quasilinear Keller–Segel system}}},
  doi          = {{10.1007/s11856-024-2618-9}},
  volume       = {{263}},
  year         = {{2024}},
}

@article{62665,
  abstract     = {{<jats:p>Structure–property relationships were studied in two coordination polymers {[Ni(bpe)(H<jats:sub>2</jats:sub>O)<jats:sub>2</jats:sub>][Ni(CN)<jats:sub>4</jats:sub>]·2 H<jats:sub>2</jats:sub>O}<jats:sub><jats:italic>n</jats:italic></jats:sub> and {[Cu(bpe)(H<jats:sub>2</jats:sub>O)<jats:sub>2</jats:sub>][Ni(CN)<jats:sub>4</jats:sub>]·ethanol}<jats:sub><jats:italic>n</jats:italic></jats:sub>. We show that the length of the ligand does not control the synthesis of Hofmann-type polymers.</jats:p>}},
  author       = {{Nguepmeni Eloundou, Valoise Brenda and Kenfack Tsobnang, Patrice and Kamgaing, Theophile and Gogoi, Chiranjib and Lopez Salas, Nieves and Bourne, Susan A.}},
  issn         = {{1466-8033}},
  journal      = {{CrystEngComm}},
  number       = {{31}},
  pages        = {{4195--4204}},
  publisher    = {{Royal Society of Chemistry (RSC)}},
  title        = {{{Crystal engineering and sorption studies on CN- and dipyridyl-bridged 2D coordination polymers}}},
  doi          = {{10.1039/d4ce00459k}},
  volume       = {{26}},
  year         = {{2024}},
}

@article{62668,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>Facile synthesis of porous carbon with high yield and high specific surface area (SSA) from low‐cost molecular precursors offers promising opportunities for their industrial applications. However, conventional activation methods using potassium and sodium hydroxides or carbonates suffer from low yields (&lt;20%) and poor control over porosity and composition especially when high SSAs are targeted (&gt;2000 m<jats:sup>2</jats:sup> g<jats:sup>−1</jats:sup>) because nanopores are typically created by etching. Herein, a non‐etching activation strategy is demonstrated using cesium salts of low‐cost carboxylic acids as the sole precursor in producing porous carbons with yields of up to 25% and SSAs reaching 3008 m<jats:sup>2</jats:sup> g<jats:sup>−1</jats:sup>. The pore size and oxygen content can be adjusted by tuning the synthesis temperature or changing the molecular precursor. Mechanistic investigation unravels the non‐classical role of cesium as an activating agent. The cesium compounds that form in situ, including carbonates, oxides, and metallic cesium, have extremely low work function enabling electron injection into organic/carbonaceous framework, promoting condensation, and intercalation of cesium ions into graphitic stacks forming slit pores. The resulting porous carbons deliver a high capacity of 252 mAh g<jats:sup>−1</jats:sup> (567 F g<jats:sup>−1</jats:sup>) and durability of 100 000 cycles as cathodes of Zn‐ion capacitors, showing their potential for electrochemical energy storage.</jats:p>}},
  author       = {{Li, Jiaxin and Xu, Yaolin and Li, Pengzhou and Völkel, Antje and Saldaña, Fernando Igoa and Antonietti, Markus and Lopez Salas, Nieves and Odziomek, Mateusz}},
  issn         = {{0935-9648}},
  journal      = {{Advanced Materials}},
  number       = {{18}},
  publisher    = {{Wiley}},
  title        = {{{Beyond Conventional Carbon Activation: Creating Porosity without Etching Using Cesium Effect}}},
  doi          = {{10.1002/adma.202311655}},
  volume       = {{36}},
  year         = {{2024}},
}

@misc{64977,
  author       = {{Mersch, Katharina Ulrike}},
  booktitle    = {{Deutsches Archiv für Erforschung des Mittelalters}},
  number       = {{2}},
  pages        = {{722}},
  title        = {{{Brown, Warren: Beyond the Monastery Walls. 2023, xiv, 385 S.: Illustrationen, Karten. - ISBN 978-1-108-47958-5}}},
  volume       = {{80}},
  year         = {{2024}},
}

@inproceedings{58131,
  author       = {{Tumat, Antje}},
  editor       = {{Höink, Dominik}},
  pages        = {{27--71}},
  publisher    = {{Textum}},
  title        = {{{Weltethos and wunderzaichen: Religion in the Music of the Western Avant-garde}}},
  year         = {{2024}},
}

@article{65535,
  abstract     = {{<jats:p>Side-channel attacks on elliptic curve cryptography (ECC) often assume a white-box attacker who has detailed knowledge of the implementation choices taken by the target implementation. Due to the complex and layered nature of ECC, there are many choices that a developer makes to obtain a functional and interoperable implementation. These include the curve model, coordinate system, addition formulas, and the scalar multiplier, or lower-level details such as the finite-field multiplication algorithm. This creates a gap between the attack requirements and a real-world attacker that often only has black-box access to the target – i.e., has no access to the source code nor knowledge of specific implementation choices made. Yet, when the gap is closed, even real-world implementations of ECC succumb to side-channel attacks, as evidenced by attacks such as TPM-Fail, Minerva, the Side Journey to Titan, or TPMScan [MSE+20; JSS+20; RLM+21; SDB+24].We study this gap by first analyzing open-source ECC libraries for insight into realworld implementation choices. We then examine the space of all ECC implementations combinatorially. Finally, we present a set of novel methods for automated reverse engineering of black-box ECC implementations and release a documented and usable open-source toolkit for side-channel analysis of ECC called pyecsca.Our methods turn attacks around: instead of attempting to recover the private key, they attempt to recover the implementation configuration given control over the private and public inputs. We evaluate them on two simulation levels and study the effect of noise on their performance. Our methods are able to 1) reverse-engineer the scalar multiplication algorithm completely and 2) infer significant information about the coordinate system and addition formulas used in a target implementation. Furthermore, they can bypass coordinate and curve randomization countermeasures.</jats:p>}},
  author       = {{Jancar, Jan and Suchanek, Vojtech and Svenda, Petr and Sedlacek, Vladimir and Chmielewski, Łukasz}},
  issn         = {{2569-2925}},
  journal      = {{IACR Transactions on Cryptographic Hardware and Embedded Systems}},
  number       = {{4}},
  pages        = {{355--381}},
  publisher    = {{Universitatsbibliothek der Ruhr-Universitat Bochum}},
  title        = {{{pyecsca: Reverse engineering black-box elliptic curve cryptography via side-channel analysis}}},
  doi          = {{10.46586/tches.v2024.i4.355-381}},
  volume       = {{2024}},
  year         = {{2024}},
}

@article{35657,
  abstract     = {{The controlled delivery of active pharmaceutical ingredients to the site of disease represents a major challenge in drug therapy. Particularly when drugs have to be transported across biological barriers, suitable drug delivery systems are of importance. In recent years responsive delivery systems have been developed which enable a controlled drug release depending on internal or external stimuli such as changes in pH, redox environment or light and temperature. In some studies delivery systems with reactivity against two different stimuli were established either to enhance the response by synergies of the stimuli or to broaden the window of possible trigger events. In the present review numerous exciting developments of pH-, light- and redox-cleavable polymers suitable for the preparation of smart delivery systems are described. The review discusses the different stimuli that can be used for a controlled drug release of polymer-based delivery systems. It puts a focus on the different polymers described for the preparation of stimuli-sensitive systems, their preparation techniques as well as their stimuli-responsive degradation. © 2022 The Authors. Polymer International published by John Wiley & Sons Ltd on behalf of Society of Industrial Chemistry.}},
  author       = {{Rust, Tarik and Jung, Dimitri and Langer, Klaus and Kuckling, Dirk}},
  issn         = {{0959-8103}},
  journal      = {{Polymer International}},
  keywords     = {{drug delivery system, stimuli, polymer, cleavable}},
  number       = {{1}},
  pages        = {{5--19}},
  publisher    = {{Wiley}},
  title        = {{{Stimuli‐accelerated polymeric drug delivery systems}}},
  doi          = {{10.1002/pi.6474}},
  volume       = {{72}},
  year         = {{2023}},
}

@article{45826,
  author       = {{Niemann, Valerie A. and Huck, Marten and Steinrück, Hans-Georg and Toney, Michael F. and Tarpeh, William A. and Bone, Sharon E.}},
  issn         = {{2690-0637}},
  journal      = {{ACS ES&T Water}},
  keywords     = {{Water Science and Technology, Environmental Chemistry, Chemistry (miscellaneous), Chemical Engineering (miscellaneous)}},
  pages        = {{2627--2637}},
  publisher    = {{American Chemical Society (ACS)}},
  title        = {{{X-ray Absorption Spectroscopy Reveals Mechanisms of Calcium and Silicon Fouling on Reverse Osmosis Membranes Used in Wastewater Reclamation}}},
  doi          = {{10.1021/acsestwater.3c00144}},
  volume       = {{3}},
  year         = {{2023}},
}

@article{47589,
  author       = {{Krämer, Felix and Paradies, Jan and Fernández, Israel and Breher, Frank}},
  issn         = {{1755-4330}},
  journal      = {{Nature Chemistry}},
  keywords     = {{General Chemical Engineering, General Chemistry}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{A crystalline aluminium–carbon-based ambiphile capable of activation and catalytic transfer of ammonia in non-aqueous media}}},
  doi          = {{10.1038/s41557-023-01340-9}},
  year         = {{2023}},
}

@inproceedings{32407,
  abstract     = {{Estimating the ground state energy of a local Hamiltonian is a central
problem in quantum chemistry. In order to further investigate its complexity
and the potential of quantum algorithms for quantum chemistry, Gharibian and Le
Gall (STOC 2022) recently introduced the guided local Hamiltonian problem
(GLH), which is a variant of the local Hamiltonian problem where an
approximation of a ground state is given as an additional input. Gharibian and
Le Gall showed quantum advantage (more precisely, BQP-completeness) for GLH
with $6$-local Hamiltonians when the guiding vector has overlap
(inverse-polynomially) close to 1/2 with a ground state. In this paper, we
optimally improve both the locality and the overlap parameters: we show that
this quantum advantage (BQP-completeness) persists even with 2-local
Hamiltonians, and even when the guiding vector has overlap
(inverse-polynomially) close to 1 with a ground state. Moreover, we show that
the quantum advantage also holds for 2-local physically motivated Hamiltonians
on a 2D square lattice. This makes a further step towards establishing
practical quantum advantage in quantum chemistry.}},
  author       = {{Gharibian, Sevag and Hayakawa, Ryu and Gall, François Le and Morimae, Tomoyuki}},
  booktitle    = {{Proceedings of the 50th EATCS International Colloquium on Automata, Languages and Programming (ICALP)}},
  number       = {{32}},
  pages        = {{1--19}},
  title        = {{{Improved Hardness Results for the Guided Local Hamiltonian Problem}}},
  doi          = {{10.4230/LIPIcs.ICALP.2023.32}},
  volume       = {{261}},
  year         = {{2023}},
}

