@article{63372,
  author       = {{Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}},
  issn         = {{0025-5874}},
  journal      = {{Mathematische Zeitschrift}},
  number       = {{1-2}},
  pages        = {{71--108}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{The small-convection limit in a two-dimensional chemotaxis-Navier–Stokes system}}},
  doi          = {{10.1007/s00209-017-1944-6}},
  volume       = {{289}},
  year         = {{2017}},
}

@article{63374,
  author       = {{Winkler, Michael}},
  issn         = {{0021-7824}},
  journal      = {{Journal de Mathématiques Pures et Appliquées}},
  pages        = {{118--169}},
  publisher    = {{Elsevier BV}},
  title        = {{{Singular structure formation in a degenerate haptotaxis model involving myopic diffusion}}},
  doi          = {{10.1016/j.matpur.2017.11.002}},
  volume       = {{112}},
  year         = {{2017}},
}

@article{63378,
  author       = {{Winkler, Michael}},
  issn         = {{1040-7294}},
  journal      = {{Journal of Dynamics and Differential Equations}},
  number       = {{1}},
  pages        = {{331--358}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{One-Dimensional Super-Fast Diffusion: Persistence Versus Extinction Revisited—Extinction at Spatial Infinity}}},
  doi          = {{10.1007/s10884-017-9577-3}},
  volume       = {{30}},
  year         = {{2017}},
}

@article{63379,
  author       = {{Winkler, Michael}},
  issn         = {{0022-0396}},
  journal      = {{Journal of Differential Equations}},
  number       = {{3}},
  pages        = {{2310--2350}},
  publisher    = {{Elsevier BV}},
  title        = {{{Renormalized radial large-data solutions to the higher-dimensional Keller–Segel system with singular sensitivity and signal absorption}}},
  doi          = {{10.1016/j.jde.2017.10.029}},
  volume       = {{264}},
  year         = {{2017}},
}

@article{63383,
  abstract     = {{<p>This paper is concerned with radially symmetric solutions of the parabolic-elliptic version of the Keller-Segel system with flux limitation, as given by <disp-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row  with Label left-parenthesis reverse-solidus star right-parenthesis EndLabel StartLayout Enlarged left-brace 1st Row  u Subscript t Baseline equals nabla dot left-parenthesis StartFraction u nabla u Over StartRoot u squared plus StartAbsoluteValue nabla u EndAbsoluteValue squared EndRoot EndFraction right-parenthesis minus chi nabla dot left-parenthesis StartFraction u nabla v Over StartRoot 1 plus StartAbsoluteValue nabla v EndAbsoluteValue squared EndRoot EndFraction right-parenthesis comma 2nd Row  0 equals normal upper Delta v minus mu plus u comma EndLayout EndLayout">
  <mml:semantics>
    <mml:mtable side="left" displaystyle="false">
      <mml:mlabeledtr>
        <mml:mtd>
          <mml:mtext>(\star)</mml:mtext>
        </mml:mtd>
        <mml:mtd>
          <mml:mrow>
            <mml:mo>{</mml:mo>
            <mml:mtable columnalign="left left" rowspacing="0.5em 0.2em" columnspacing="1em" displaystyle="false">
              <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:mstyle scriptlevel="0">
                    <mml:mrow class="MJX-TeXAtom-ORD">
                      <mml:mo maxsize="1.623em" minsize="1.623em">(</mml:mo>
                    </mml:mrow>
                  </mml:mstyle>
                  <mml:mfrac>
                    <mml:mrow>
                      <mml:mi>u</mml:mi>
                      <mml:mi mathvariant="normal">∇<!-- ∇ --></mml:mi>
                      <mml:mi>u</mml:mi>
                    </mml:mrow>
                    <mml:msqrt>
                      <mml:msup>
                        <mml:mi>u</mml:mi>
                        <mml:mn>2</mml:mn>
                      </mml:msup>
                      <mml:mo>+</mml:mo>
                      <mml:mrow class="MJX-TeXAtom-ORD">
                        <mml:mo stretchy="false">|</mml:mo>
                      </mml:mrow>
                      <mml:mi mathvariant="normal">∇<!-- ∇ --></mml:mi>
                      <mml:mi>u</mml:mi>
                      <mml:msup>
                        <mml:mrow class="MJX-TeXAtom-ORD">
                          <mml:mo stretchy="false">|</mml:mo>
                        </mml:mrow>
                        <mml:mn>2</mml:mn>
                      </mml:msup>
                    </mml:msqrt>
                  </mml:mfrac>
                  <mml:mstyle scriptlevel="0">
                    <mml:mrow class="MJX-TeXAtom-ORD">
                      <mml:mo maxsize="1.623em" minsize="1.623em">)</mml:mo>
                    </mml:mrow>
                  </mml:mstyle>
                  <mml:mo>−<!-- − --></mml:mo>
                  <mml:mi>χ<!-- χ --></mml:mi>
                  <mml:mspace width="thinmathspace" />
                  <mml:mi mathvariant="normal">∇<!-- ∇ --></mml:mi>
                  <mml:mo>⋅<!-- ⋅ --></mml:mo>
                  <mml:mstyle scriptlevel="0">
                    <mml:mrow class="MJX-TeXAtom-ORD">
                      <mml:mo maxsize="1.623em" minsize="1.623em">(</mml:mo>
                    </mml:mrow>
                  </mml:mstyle>
                  <mml:mfrac>
                    <mml:mrow>
                      <mml:mi>u</mml:mi>
                      <mml:mi mathvariant="normal">∇<!-- ∇ --></mml:mi>
                      <mml:mi>v</mml:mi>
                    </mml:mrow>
                    <mml:msqrt>
                      <mml:mn>1</mml:mn>
                      <mml:mo>+</mml:mo>
                      <mml:mrow class="MJX-TeXAtom-ORD">
                        <mml:mo stretchy="false">|</mml:mo>
                      </mml:mrow>
                      <mml:mi mathvariant="normal">∇<!-- ∇ --></mml:mi>
                      <mml:mi>v</mml:mi>
                      <mml:msup>
                        <mml:mrow class="MJX-TeXAtom-ORD">
                          <mml:mo stretchy="false">|</mml:mo>
                        </mml:mrow>
                        <mml:mn>2</mml:mn>
                      </mml:msup>
                    </mml:msqrt>
                  </mml:mfrac>
                  <mml:mstyle scriptlevel="0">
                    <mml:mrow class="MJX-TeXAtom-ORD">
                      <mml:mo maxsize="1.623em" minsize="1.623em">)</mml:mo>
                    </mml:mrow>
                  </mml:mstyle>
                  <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<!-- Δ --></mml:mi>
                  <mml:mi>v</mml:mi>
                  <mml:mo>−<!-- − --></mml:mo>
                  <mml:mi>μ<!-- μ --></mml:mi>
                  <mml:mo>+</mml:mo>
                  <mml:mi>u</mml:mi>
                  <mml:mo>,</mml:mo>
                </mml:mtd>
              </mml:mtr>
            </mml:mtable>
            <mml:mo fence="true" stretchy="true" symmetric="true" />
          </mml:mrow>
        </mml:mtd>
      </mml:mlabeledtr>
    </mml:mtable>
    <mml:annotation encoding="application/x-tex">\begin{equation}\tag {\star } \begin {cases} u_t=\nabla \cdot \Big (\frac {u\nabla u}{\sqrt {u^2+|\nabla u|^2}}\Big ) - \chi \, \nabla \cdot \Big (\frac {u\nabla v}{\sqrt {1+|\nabla v|^2}}\Big ), \\[3pt] 0=\Delta v - \mu + u, \end{cases} \end{equation}</mml:annotation>
  </mml:semantics>
</mml:math>
</disp-formula>
 under the initial condition <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u vertical-bar Subscript t equals 0 Baseline equals u 0 greater-than 0">
  <mml:semantics>
    <mml:mrow>
      <mml:mi>u</mml:mi>
      <mml:msub>
        <mml:mrow class="MJX-TeXAtom-ORD">
          <mml:mo stretchy="false">|</mml:mo>
        </mml:mrow>
        <mml:mrow class="MJX-TeXAtom-ORD">
          <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:mo>&gt;</mml:mo>
      <mml:mn>0</mml:mn>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">u|_{t=0}=u_0&gt;0</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula> and no-flux boundary conditions in a ball <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Omega subset-of double-struck upper R Superscript n">
  <mml:semantics>
    <mml:mrow>
      <mml:mi mathvariant="normal">Ω<!-- Ω --></mml:mi>
      <mml:mo>⊂<!-- ⊂ --></mml:mo>
      <mml:msup>
        <mml:mrow class="MJX-TeXAtom-ORD">
          <mml:mi mathvariant="double-struck">R</mml:mi>
        </mml:mrow>
        <mml:mi>n</mml:mi>
      </mml:msup>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">\Omega \subset \mathbb {R}^n</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula>, where <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="chi greater-than 0">
  <mml:semantics>
    <mml:mrow>
      <mml:mi>χ<!-- χ --></mml:mi>
      <mml:mo>&gt;</mml:mo>
      <mml:mn>0</mml:mn>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">\chi &gt;0</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula> and <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="mu colon equals StartFraction 1 Over StartAbsoluteValue normal upper Omega EndAbsoluteValue EndFraction integral Underscript normal upper Omega Endscripts u 0">
  <mml:semantics>
    <mml:mrow>
      <mml:mi>μ<!-- μ --></mml:mi>
      <mml:mo>:=</mml:mo>
      <mml:mfrac>
        <mml:mn>1</mml:mn>
        <mml:mrow>
          <mml:mrow class="MJX-TeXAtom-ORD">
            <mml:mo stretchy="false">|</mml:mo>
          </mml:mrow>
          <mml:mi mathvariant="normal">Ω<!-- Ω --></mml:mi>
          <mml:mrow class="MJX-TeXAtom-ORD">
            <mml:mo stretchy="false">|</mml:mo>
          </mml:mrow>
        </mml:mrow>
      </mml:mfrac>
      <mml:msub>
        <mml:mo>∫<!-- ∫ --></mml:mo>
        <mml:mi mathvariant="normal">Ω<!-- Ω --></mml:mi>
      </mml:msub>
      <mml:msub>
        <mml:mi>u</mml:mi>
        <mml:mn>0</mml:mn>
      </mml:msub>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">\mu :=\frac {1}{|\Omega |} \int _\Omega u_0</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula>. A previous result of the authors [Comm. Partial Differential Equations 42 (2017), 436–473] has asserted global existence of bounded classical solutions for arbitrary positive radial initial data <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u 0 element-of upper C cubed left-parenthesis normal upper Omega overbar right-parenthesis">
  <mml:semantics>
    <mml:mrow>
      <mml:msub>
        <mml:mi>u</mml:mi>
        <mml:mn>0</mml:mn>
      </mml:msub>
      <mml:mo>∈<!-- ∈ --></mml:mo>
      <mml:msup>
        <mml:mi>C</mml:mi>
        <mml:mn>3</mml:mn>
      </mml:msup>
      <mml:mo stretchy="false">(</mml:mo>
      <mml:mrow class="MJX-TeXAtom-ORD">
        <mml:mover>
          <mml:mi mathvariant="normal">Ω<!-- Ω --></mml:mi>
          <mml:mo stretchy="false">¯<!-- ¯ --></mml:mo>
        </mml:mover>
      </mml:mrow>
      <mml:mo stretchy="false">)</mml:mo>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">u_0\in C^3(\bar \Omega )</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula> when either <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n greater-than-or-equal-to 2">
  <mml:semantics>
    <mml:mrow>
      <mml:mi>n</mml:mi>
      <mml:mo>≥<!-- ≥ --></mml:mo>
      <mml:mn>2</mml:mn>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">n\ge 2</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula> and <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="chi greater-than 1">
  <mml:semantics>
    <mml:mrow>
      <mml:mi>χ<!-- χ --></mml:mi>
      <mml:mo>&gt;</mml:mo>
      <mml:mn>1</mml:mn>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">\chi &gt;1</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula>, or <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n equals 1">
  <mml:semantics>
    <mml:mrow>
      <mml:mi>n</mml:mi>
      <mml:mo>=</mml:mo>
      <mml:mn>1</mml:mn>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">n=1</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula> and <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Underscript normal upper Omega Endscripts u 0 greater-than StartFraction 1 Over StartRoot left-parenthesis chi squared minus 1 right-parenthesis Subscript plus Baseline EndRoot EndFraction">
  <mml:semantics>
    <mml:mrow>
      <mml:msub>
        <mml:mo>∫<!-- ∫ --></mml:mo>
        <mml:mi mathvariant="normal">Ω<!-- Ω --></mml:mi>
      </mml:msub>
      <mml:msub>
        <mml:mi>u</mml:mi>
        <mml:mn>0</mml:mn>
      </mml:msub>
      <mml:mo>&gt;</mml:mo>
      <mml:mfrac>
        <mml:mn>1</mml:mn>
        <mml:msqrt>
          <mml:mo stretchy="false">(</mml:mo>
          <mml:msup>
            <mml:mi>χ<!-- χ --></mml:mi>
            <mml:mn>2</mml:mn>
          </mml:msup>
          <mml:mo>−<!-- − --></mml:mo>
          <mml:mn>1</mml:mn>
          <mml:msub>
            <mml:mo stretchy="false">)</mml:mo>
            <mml:mo>+</mml:mo>
          </mml:msub>
        </mml:msqrt>
      </mml:mfrac>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">\int _\Omega u_0&gt;\frac {1}{\sqrt {(\chi ^2-1)_+}}</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula>.</p>

<p>This present paper shows that these conditions are essentially optimal: Indeed, it is shown that if the taxis coefficient satisfies <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="chi greater-than 1">
  <mml:semantics>
    <mml:mrow>
      <mml:mi>χ<!-- χ --></mml:mi>
      <mml:mo>&gt;</mml:mo>
      <mml:mn>1</mml:mn>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">\chi &gt;1</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula>, then for any choice of <disp-formula content-type="math/mathml">
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout Enlarged left-brace 1st Row 1st Column m greater-than StartFraction 1 Over StartRoot chi squared minus 1 EndRoot EndFraction 2nd Column a m p semicolon if n equals 1 comma 2nd Row 1st Column m greater-than 0 is arbitrary 2nd Column a m p semicolon if n greater-than-or-equal-to 2 comma EndLayout">
  <mml:semantics>
    <mml:mrow>
      <mml:mo>{</mml:mo>
      <mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false">
        <mml:mtr>
          <mml:mtd>
            <mml:mi>m</mml:mi>
            <mml:mo>&gt;</mml:mo>
            <mml:mfrac>
              <mml:mn>1</mml:mn>
              <mml:msqrt>
                <mml:msup>
                  <mml:mi>χ<!-- χ --></mml:mi>
                  <mml:mn>2</mml:mn>
                </mml:msup>
                <mml:mo>−<!-- − --></mml:mo>
                <mml:mn>1</mml:mn>
              </mml:msqrt>
            </mml:mfrac>
          </mml:mtd>
          <mml:mtd>
            <mml:mi>a</mml:mi>
            <mml:mi>m</mml:mi>
            <mml:mi>p</mml:mi>
            <mml:mo>;</mml:mo>
            <mml:mrow>
              <mml:mtext>if </mml:mtext>
              <mml:mrow class="MJX-TeXAtom-ORD">
                <mml:mi>n</mml:mi>
                <mml:mo>=</mml:mo>
                <mml:mn>1</mml:mn>
              </mml:mrow>
            </mml:mrow>
            <mml:mo>,</mml:mo>
          </mml:mtd>
        </mml:mtr>
        <mml:mtr>
          <mml:mtd>
            <mml:mrow>
              <mml:mrow class="MJX-TeXAtom-ORD">
                <mml:mi>m</mml:mi>
                <mml:mo>&gt;</mml:mo>
                <mml:mn>0</mml:mn>
              </mml:mrow>
              <mml:mtext> is arbitrary</mml:mtext>
            </mml:mrow>
          </mml:mtd>
          <mml:mtd>
            <mml:mi>a</mml:mi>
            <mml:mi>m</mml:mi>
            <mml:mi>p</mml:mi>
            <mml:mo>;</mml:mo>
            <mml:mrow>
              <mml:mtext>if </mml:mtext>
              <mml:mrow class="MJX-TeXAtom-ORD">
                <mml:mi>n</mml:mi>
                <mml:mo>≥<!-- ≥ --></mml:mo>
                <mml:mn>2</mml:mn>
              </mml:mrow>
            </mml:mrow>
            <mml:mo>,</mml:mo>
          </mml:mtd>
        </mml:mtr>
      </mml:mtable>
      <mml:mo fence="true" stretchy="true" symmetric="true" />
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">\begin {cases} m&gt;\frac {1}{\sqrt {\chi ^2-1}} &amp; \text {if $n=1$}, \\ \text {$m&gt;0$ is arbitrary} &amp; \text {if $n\ge 2$}, \end {cases}</mml:annotation>
  </mml:semantics>
</mml:math>
\]
</disp-formula> there exist positive initial data <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u 0 element-of upper C cubed left-parenthesis normal upper Omega overbar right-parenthesis">
  <mml:semantics>
    <mml:mrow>
      <mml:msub>
        <mml:mi>u</mml:mi>
        <mml:mn>0</mml:mn>
      </mml:msub>
      <mml:mo>∈<!-- ∈ --></mml:mo>
      <mml:msup>
        <mml:mi>C</mml:mi>
        <mml:mn>3</mml:mn>
      </mml:msup>
      <mml:mo stretchy="false">(</mml:mo>
      <mml:mrow class="MJX-TeXAtom-ORD">
        <mml:mover>
          <mml:mi mathvariant="normal">Ω<!-- Ω --></mml:mi>
          <mml:mo stretchy="false">¯<!-- ¯ --></mml:mo>
        </mml:mover>
      </mml:mrow>
      <mml:mo stretchy="false">)</mml:mo>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">u_0\in C^3(\bar \Omega )</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula> satisfying <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Underscript normal upper Omega Endscripts u 0 equals m">
  <mml:semantics>
    <mml:mrow>
      <mml:msub>
        <mml:mo>∫<!-- ∫ --></mml:mo>
        <mml:mi mathvariant="normal">Ω<!-- 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:annotation encoding="application/x-tex">\int _\Omega u_0=m</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula> which are such that for some <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T greater-than 0">
  <mml:semantics>
    <mml:mrow>
      <mml:mi>T</mml:mi>
      <mml:mo>&gt;</mml:mo>
      <mml:mn>0</mml:mn>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">T&gt;0</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula>, (<inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="star">
  <mml:semantics>
    <mml:mo>⋆<!-- ⋆ --></mml:mo>
    <mml:annotation encoding="application/x-tex">\star</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula>) possesses a uniquely determined classical solution <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis u comma v right-parenthesis">
  <mml:semantics>
    <mml:mrow>
      <mml:mo stretchy="false">(</mml:mo>
      <mml:mi>u</mml:mi>
      <mml:mo>,</mml:mo>
      <mml:mi>v</mml:mi>
      <mml:mo stretchy="false">)</mml:mo>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">(u,v)</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula> in <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Omega times left-parenthesis 0 comma upper T right-parenthesis">
  <mml:semantics>
    <mml:mrow>
      <mml:mi mathvariant="normal">Ω<!-- Ω --></mml:mi>
      <mml:mo>×<!-- × --></mml:mo>
      <mml:mo stretchy="false">(</mml:mo>
      <mml:mn>0</mml:mn>
      <mml:mo>,</mml:mo>
      <mml:mi>T</mml:mi>
      <mml:mo stretchy="false">)</mml:mo>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">\Omega \times (0,T)</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula> blowing up at time <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T">
  <mml:semantics>
    <mml:mi>T</mml:mi>
    <mml:annotation encoding="application/x-tex">T</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula> in the sense that <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="limit sup double-vertical-bar u left-parenthesis dot comma t right-parenthesis double-vertical-bar Subscript upper L Sub Superscript normal infinity Subscript left-parenthesis normal upper Omega right-parenthesis Baseline equals normal infinity">
  <mml:semantics>
    <mml:mrow>
      <mml:munder>
        <mml:mo movablelimits="true" form="prefix">lim sup</mml:mo>
        <mml:mrow class="MJX-TeXAtom-ORD">
          <mml:mi>t</mml:mi>
          <mml:mo stretchy="false">↗<!-- ↗ --></mml:mo>
          <mml:mi>T</mml:mi>
        </mml:mrow>
      </mml:munder>
      <mml:mo fence="false" stretchy="false">‖<!-- ‖ --></mml:mo>
      <mml:mi>u</mml:mi>
      <mml:mo stretchy="false">(</mml:mo>
      <mml:mo>⋅<!-- ⋅ --></mml:mo>
      <mml:mo>,</mml:mo>
      <mml:mi>t</mml:mi>
      <mml:mo stretchy="false">)</mml:mo>
      <mml:msub>
        <mml:mo fence="false" stretchy="false">‖<!-- ‖ --></mml:mo>
        <mml:mrow class="MJX-TeXAtom-ORD">
          <mml:msup>
            <mml:mi>L</mml:mi>
            <mml:mi mathvariant="normal">∞<!-- ∞ --></mml:mi>
          </mml:msup>
          <mml:mo stretchy="false">(</mml:mo>
          <mml:mi mathvariant="normal">Ω<!-- Ω --></mml:mi>
          <mml:mo stretchy="false">)</mml:mo>
        </mml:mrow>
      </mml:msub>
      <mml:mo>=</mml:mo>
      <mml:mi mathvariant="normal">∞<!-- ∞ --></mml:mi>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">\limsup _{t\nearrow T} \|u(\cdot ,t)\|_{L^\infty (\Omega )}=\infty</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula>.</p>

<p>This result is derived by means of a comparison argument applied to the doubly degenerate scalar parabolic equation satisfied by the mass accumulation function associated with (<inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="star">
  <mml:semantics>
    <mml:mo>⋆<!-- ⋆ --></mml:mo>
    <mml:annotation encoding="application/x-tex">\star</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula>).</p>}},
  author       = {{Bellomo, Nicola and Winkler, Michael}},
  issn         = {{2330-0000}},
  journal      = {{Transactions of the American Mathematical Society, Series B}},
  number       = {{2}},
  pages        = {{31--67}},
  publisher    = {{American Mathematical Society (AMS)}},
  title        = {{{Finite-time blow-up in a degenerate chemotaxis system with flux limitation}}},
  doi          = {{10.1090/btran/17}},
  volume       = {{4}},
  year         = {{2017}},
}

@article{63040,
  author       = {{Thevenard, L. and Boutigny, B. and Güsken, Nicholas Alexander and Becerra, L. and Ulysse, C. and Shihab, S. and Lemaître, A. and Kim, J.-V. and Jeudy, V. and Gourdon, C.}},
  issn         = {{2469-9950}},
  journal      = {{Physical Review B}},
  number       = {{5}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Spin transfer and spin-orbit torques in in-plane magnetized (Ga,Mn)As tracks}}},
  doi          = {{10.1103/physrevb.95.054422}},
  volume       = {{95}},
  year         = {{2017}},
}

@article{59497,
  abstract     = {{<p>High-quality Al/InAs and Nb/InAs superconducting hybrid structure interfaces on catalyst free InAs nanowires.</p>}},
  author       = {{Güsken, Nicholas Alexander and Rieger, Torsten and Zellekens, Patrick and Bennemann, Benjamin and Neumann, Elmar and Lepsa, Mihail I. and Schäpers, Thomas and Grützmacher, Detlev}},
  issn         = {{2040-3364}},
  journal      = {{Nanoscale}},
  number       = {{43}},
  pages        = {{16735--16741}},
  publisher    = {{Royal Society of Chemistry (RSC)}},
  title        = {{{MBE growth of Al/InAs and Nb/InAs superconducting hybrid nanowire structures}}},
  doi          = {{10.1039/c7nr03982d}},
  volume       = {{9}},
  year         = {{2017}},
}

@article{57146,
  author       = {{Bürgel, Christoph and Siepmann, Dirk and Diversy, Sascha }},
  journal      = {{International Journal of Lexicography}},
  number       = {{1}},
  pages        = {{63--84}},
  title        = {{{The Corpus de référence du français contemporain (CRFC) as the first genre-diverse mega-corpus of French }}},
  volume       = {{30}},
  year         = {{2017}},
}

@book{57148,
  editor       = {{Bürgel, Christoph and Reimann, Daniel }},
  title        = {{{Sprachliche Mittel im Unterricht der romanischen Sprachen. Aussprache, Wortschatz und Morphosyntax in Zeiten der Kompetenzorientierung}}},
  year         = {{2017}},
}

@article{57145,
  author       = {{Bürgel, Christoph}},
  journal      = {{Der fremdsprachliche Unterricht Französisch}},
  pages        = {{9--15}},
  title        = {{{Ça vaut le coup – c’est sûr et certain ! Mit Phrasemen zu natürlichem Sprachgebrauch}}},
  year         = {{2017}},
}

@inbook{57234,
  author       = {{Meise, Bianca and Schloots, Franziska Margarete and Müller-Lietzkow, Jörg and Meister, Dorothee M.}},
  booktitle    = {{Interdisziplinäre Perspektiven zur Zukunft der Wertschöpfung}},
  isbn         = {{9783658202644}},
  publisher    = {{Springer Fachmedien Wiesbaden}},
  title        = {{{Interdisziplinäres Projektmanagement – Strategische Handlungsempfehlungen für Kooperationsverbünde in akademischen Kontexten}}},
  doi          = {{10.1007/978-3-658-20265-1_18}},
  year         = {{2017}},
}

@misc{56129,
  author       = {{Priesching, Nicole}},
  booktitle    = {{Rottenburger Jahrbuch für Kirchengeschichte}},
  pages        = {{360–361}},
  title        = {{{Otto Weiß: Die Macht der Seherin von Altötting. Geisterglaube im Katholizismus des 19. Jahrhunderts. Kevelaer 2015}}},
  volume       = {{36}},
  year         = {{2017}},
}

@inproceedings{47002,
  author       = {{Güldenpenning, Iris and Kunde, W. and Weigelt, Matthias}},
  booktitle    = {{Abstracts der 49. Jahrestagung der Arbeitsgemeinschaft für Sportpsychologie}},
  editor       = {{Zuber, C. and Schmid, J. and Schmidt, M. and Wegner, M. and Conzelmann, A.}},
  location     = {{Bern}},
  pages        = {{42--43}},
  title        = {{{Ist der Blicktäuschungseffekt im  Basketball robust gegenüber Übungseffekten?}}},
  year         = {{2017}},
}

@inproceedings{46999,
  author       = {{Güldenpenning, Iris and Alhaj Ahmad Alaboud, M. and Steggemann-Weinrich, Y. and Kunde, W. and Weigelt, Matthias}},
  booktitle    = {{Abstracts of the 59th Conference of Experimental Psychologists (TeaP)}},
  editor       = {{Goschke, T. and Bolte, A. and Kirschbaum, C.}},
  location     = {{Dresden}},
  pages        = {{58--59}},
  publisher    = {{Pabst Science Publishers}},
  title        = {{{Head fake or Blicktäuschung? Investigating the source of information  conflict during fake action in sports}}},
  year         = {{2017}},
}

@inproceedings{47004,
  author       = {{Güldenpenning, Iris and Alhaj Ahmad Alaboud, M. and Steggemann-Weinrich, Y. and Kunde, W. and Weigelt, Matthias}},
  booktitle    = {{Tagungsband des 23. Hochschultag}},
  editor       = {{Schwirtz, A. and Mess, F. and Demetriou, Y. and Senner, V.}},
  publisher    = {{Feldhaus Verlag}},
  title        = {{{Head fake or Blicktäuschung? Investigating the source of information  conflict during fake action in sports}}},
  year         = {{2017}},
}

@inproceedings{55056,
  author       = {{Speck, René and Ngomo, Axel-Cyrille Ngonga}},
  booktitle    = {{Proceedings of the 9th Knowledge Capture Conference}},
  pages        = {{1–4}},
  title        = {{{Ensemble learning of named entity recognition algorithms using multilayer perceptron for the multilingual web of data}}},
  year         = {{2017}},
}

@inbook{57749,
  author       = {{Langer, Antje}},
  booktitle    = {{Sexualität und Soziale Arbeit}},
  editor       = {{Klein, Alexandra and Tuider, Elisabeth}},
  isbn         = {{978-3-8340-1706-2}},
  pages        = {{149--163}},
  publisher    = {{Schneider Verlag Hohengehren}},
  title        = {{{Arbeit an und mit Widersprüchen – Zur Herstellung und Aufrechterhaltung einer sexualpädagogischen Situation.}}},
  volume       = {{40}},
  year         = {{2017}},
}

@article{57747,
  author       = {{Langer, Antje}},
  journal      = {{Zeitschrift für Soziologie der Sozialisation und Erziehung (ZSE)}},
  number       = {{1}},
  title        = {{{Körperlichkeit in der Machtasymmetrie pädagogischer Verhältnisse.}}},
  volume       = {{37}},
  year         = {{2017}},
}

@article{57746,
  author       = {{Langer, Antje}},
  journal      = {{Zeitschrift für Sexualforschung (Z Sexualforsch)}},
  number       = {{4}},
  title        = {{{„Die brauchen was zum Ausprobieren”. Körper und Körper-Modelle in der sexualpädagogischen Praxis. }}},
  volume       = {{30}},
  year         = {{2017}},
}

@article{45142,
  author       = {{Wöhrle, J. and Franke, Sebastian and Kissgen, R.}},
  journal      = {{Rehabilitation Psychology}},
  number       = {{1}},
  pages        = {{83–91}},
  title        = {{{The German Multidimensional Attitude Scale Toward Persons With Disabilities (G-MAS): A Factor Analytical Study Among High-School Students}}},
  doi          = {{10.1037/rep0000170}},
  volume       = {{63}},
  year         = {{2017}},
}