@article{63139,
author = {{Iyengar, Srikanth B. and Letz, Janina Carmen and Liu, Jian and Pollitz, Josh}},
issn = {{0030-8730}},
journal = {{Pacific J. Math.}},
number = {{2}},
pages = {{275--293}},
title = {{{Exceptional complete intersection maps of local rings}}},
doi = {{10.2140/pjm.2022.318.275}},
volume = {{318}},
year = {{2022}},
}
@proceedings{55135,
editor = {{Jonas, Kristina and Quinting, Jana and Gerhards, Lisa and Hüsgen, Anne and Rubi-Fessen, Ilona and Stenneken, Prisca and Rosenkranz, Anna}},
title = {{{Kommunikation – Sprache, Emotion, Kognition}}},
year = {{2022}},
}
@article{63175,
author = {{Barlovits, S and Caldeira, A and Fesakis, G and Jablonski, S and Filippaki, DK and Lázaro, C and Ludwig, M and Mammana, MF and Moura, A and Oehler, DXK and Recio, T and Taranto, E and Volika, S}},
issn = {{2227-7390}},
number = {{10}},
title = {{{Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment}}},
volume = {{10}},
year = {{2022}},
}
@article{63174,
author = {{Barbosa, A and Vale, I and Jablonski, S and Ludwig, M}},
issn = {{2227-7102}},
number = {{5}},
title = {{{Walking through Algebraic Thinking with Theme-Based (Mobile) Math Trails}}},
volume = {{12}},
year = {{2022}},
}
@book{36424,
abstract = {{Das Oratorium kann als wichtige Gattung für die Analyse des Zusammenspiels von Religion und Politik im Medium der Musik gelten. Die Studie wendet sich dem Verhältnis dieser religiösen Musikform zum deutschen Nationalismus vom Beginn des Ersten bis zum Ende des Zweiten Weltkriegs zu. Im Fokus stehen verschiedene Weisen der Instrumentalisierung von Musik, etwa zur ‚Heldenehrung‘, zur Bildung einer ‚vorgestellten Gemeinschaft‘ oder zur Gewinnung der Arbeiterschaft. Bei der Analyse der Politisierung des Oratoriums sind vier Beobachtungsperspektiven leitend: Konfession, Säkularisierung, Erinnerungskultur und Vergemeinschaftung.
Entsprechend liegt der Schwerpunkt der Studie auf der Analyse der sozialgeschichtlichen Funktion der Gattung. Daneben jedoch werden – in Form von Fallstudien zu bisher unerforschten Werken – auch musikalische Detailanalysen durchgeführt, die das in der jeweiligen Komposition realisierte Verhältnis von religiösen und nationalistischen Elementen offenlegen. }},
author = {{Höink, Dominik}},
isbn = {{978-3-8309-3984-9}},
pages = {{590}},
publisher = {{Waxmann Verlag}},
title = {{{Oratorium und Nation (1914–1945) }}},
volume = {{8}},
year = {{2022}},
}
@inbook{34705,
abstract = {{n 1789, Eberhard repudiated Kant’s claim expressed in the first edition of his Critique of Pure Reason to have delivered a new, namely transcendental turn in philosophy, as he was able to retrace our cognition to the origin of phenomena instead of delivering a “merely logical deduction”. Eberhard holds that there was nothing new, but all delivered in Leibniz and Wolff; to prove his claim he refers to a quote from Du Châtelet, taken from a paragraph where she determines the right understanding as to be able “to penetrate to the origin of phenomena”. This paper brings Du Châtelet into discourse with Kant via this Eberhard quote. In its first part, it investigates the use of her quote in the Kant-Eberhard controversy. The second part serves to ground the quote in Du Châtelet’s epistemology. It lays out how to understand Du Châtelet’s claim to penetrate to the origin of phenomena. Du Châtelet’s claim to have renewed philosophy must be taken seriously, and it is helpful for rethinking the German philosophical development from the rationalists to Kant through including Du Châtelet’s theory of cognition.}},
author = {{Hagengruber, Ruth Edith}},
booktitle = {{Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749)}},
editor = {{Hagengruber, Ruth Edith}},
isbn = {{9783030899202}},
issn = {{2523-8760}},
keywords = {{Émilie Du Châtelet, History of Science, Newton, Kant, Eberhard, Wolff, Leibniz}},
pages = {{57--84}},
publisher = {{Springer International Publishing}},
title = {{{Du Châtelet and Kant: Claiming the Renewal of Philosophy}}},
doi = {{10.1007/978-3-030-89921-9_3}},
volume = {{10}},
year = {{2022}},
}
@inbook{63184,
author = {{Hagengruber, Ruth}},
booktitle = {{Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749)}},
editor = {{Hagengruber, Ruth Edith}},
isbn = {{9783030899202}},
issn = {{2523-8760}},
pages = {{1--20}},
publisher = {{Springer International Publishing}},
title = {{{An Introduction to the Volume}}},
doi = {{10.1007/978-3-030-89921-9_1}},
volume = {{10}},
year = {{2022}},
}
@article{63206,
abstract = {{AbstractPure iron is very attractive as a biodegradable implant material due to its high biocompatibility. In combination with additive manufacturing, which facilitates great flexibility of the implant design, it is possible to selectively adjust the microstructure of the material in the process, thereby control the corrosion and fatigue behavior. In the present study, conventional hot-rolled (HR) pure iron is compared to pure iron manufactured by electron beam melting (EBM). The microstructure, the corrosion behavior and the fatigue properties were studied comprehensively. The investigated sample conditions showed significant differences in the microstructures that led to changes in corrosion and fatigue properties. The EBM iron showed significantly lower fatigue strength compared to the HR iron. These different fatigue responses were observed under purely mechanical loading as well as with superimposed corrosion influence and are summarized in a model that describes the underlying failure mechanisms.}},
author = {{Wackenrohr, Steffen and Torrent, Christof Johannes Jaime and Herbst, Sebastian and Nürnberger, Florian and Krooss, Philipp and Ebbert, Christoph and Voigt, Markus and Grundmeier, Guido and Niendorf, Thomas and Maier, Hans Jürgen}},
issn = {{2397-2106}},
journal = {{npj Materials Degradation}},
number = {{1}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Corrosion fatigue behavior of electron beam melted iron in simulated body fluid}}},
doi = {{10.1038/s41529-022-00226-4}},
volume = {{6}},
year = {{2022}},
}
@article{33670,
author = {{Schapeler, Timon and Bartley, Tim}},
issn = {{2469-9926}},
journal = {{Physical Review A}},
number = {{1}},
publisher = {{American Physical Society (APS)}},
title = {{{Information extraction in photon-counting experiments}}},
doi = {{10.1103/physreva.106.013701}},
volume = {{106}},
year = {{2022}},
}
@article{63234,
author = {{Wiegmann, Jens and Leppin, Christian and Langhoff, Arne and Schwaderer, Jan and Beuermann, Sabine and Johannsmann, Diethelm and Weber, Alfred P.}},
issn = {{0921-8831}},
journal = {{Advanced Powder Technology}},
number = {{3}},
publisher = {{Elsevier BV}},
title = {{{Influence of the solvent evaporation rate on the β-Phase content of electrosprayed PVDF particles and films studied by a fast Multi-Overtone QCM}}},
doi = {{10.1016/j.apt.2022.103452}},
volume = {{33}},
year = {{2022}},
}
@article{63233,
author = {{Leppin, Christian and Langhoff, Arne and Johannsmann, Diethelm}},
issn = {{0003-2700}},
journal = {{Analytical Chemistry}},
number = {{28}},
pages = {{10227--10233}},
publisher = {{American Chemical Society (ACS)}},
title = {{{Square-Wave Electrogravimetry Combined with Voltammetry Reveals Reversible Submonolayer Adsorption of Redox-Active Ions}}},
doi = {{10.1021/acs.analchem.2c01763}},
volume = {{94}},
year = {{2022}},
}
@article{63310,
abstract = {{AbstractThe chemotaxis–Stokes systemnt+u⋅∇n=∇⋅(D(n)∇n)−∇⋅(nS(x,n,c)⋅∇c),ct+u⋅∇c=Δc−nc,ut=Δu+∇P+n∇Φ,∇⋅u=0,\left\{\begin{array}{l}{n}_{t}+u\cdot \nabla n=\nabla \cdot (D\left(n)\nabla n)-\nabla \cdot (nS\left(x,n,c)\cdot \nabla c),\\ {c}_{t}+u\cdot \nabla c=\Delta c-nc,\\ {u}_{t}=\Delta u+\nabla P+n\nabla \Phi ,\hspace{1.0em}\nabla \cdot u=0,\end{array}\right.is considered in a smoothly bounded convex domainΩ⊂R3\Omega \subset {{\mathbb{R}}}^{3}, with given suitably regular functionsD:[0,∞)→[0,∞)D:{[}0,\infty )\to {[}0,\infty ),S:Ω¯×[0,∞)×(0,∞)→R3×3S:\overline{\Omega }\times {[}0,\infty )\times \left(0,\infty )\to {{\mathbb{R}}}^{3\times 3}andΦ:Ω¯→R\Phi :\overline{\Omega }\to {\mathbb{R}}such thatD>0D\gt 0on(0,∞)\left(0,\infty ). It is shown that if with some nondecreasingS0:(0,∞)→(0,∞){S}_{0}:\left(0,\infty )\to \left(0,\infty )we have∣S(x,n,c)∣≤S0(c)c12for all(x,n,c)∈Ω¯×[0,∞)×(0,∞),| S\left(x,n,c)| \le \frac{{S}_{0}\left(c)}{{c}^{\tfrac{1}{2}}}\hspace{1.0em}\hspace{0.1em}\text{for all}\hspace{0.1em}\hspace{0.33em}\left(x,n,c)\in \overline{\Omega }\times {[}0,\infty )\times \left(0,\infty ),then for allM>0M\gt 0there existsL(M)>0L\left(M)\gt 0such that wheneverliminfn→∞D(n)>L(M)andliminfn↘0D(n)n>0,\mathop{\mathrm{liminf}}\limits_{n\to \infty }D\left(n)\gt L\left(M)\hspace{1.0em}\hspace{0.1em}\text{and}\hspace{0.1em}\hspace{1.0em}\mathop{\mathrm{liminf}}\limits_{n\searrow 0}\frac{D\left(n)}{n}\gt 0,for all sufficiently regular initial data(n0,c0,u0)\left({n}_{0},{c}_{0},{u}_{0})fulfilling‖c0‖L∞(Ω)≤M\Vert {c}_{0}{\Vert }_{{L}^{\infty }\left(\Omega )}\le Man associated no-flux/no-flux/Dirichlet initial-boundary value problem admits a global bounded weak solution, classical if additionallyD(0)>0D\left(0)\gt 0. When combined with previously known results, this particularly implies global existence of bounded solutions whenD(n)=nm−1D\left(n)={n}^{m-1},n≥0n\ge 0, with arbitrarym>1m\gt 1, but beyond this asserts global boundedness also in the presence of diffusivities which exhibit arbitrarily slow divergence to+∞+\inftyat large densities and of possibly singular chemotactic sensitivities.}},
author = {{Winkler, Michael}},
issn = {{2169-0375}},
journal = {{Advanced Nonlinear Studies}},
number = {{1}},
pages = {{88--117}},
publisher = {{Walter de Gruyter GmbH}},
title = {{{Chemotaxis-Stokes interaction with very weak diffusion enhancement: Blow-up exclusion via detection of absorption-induced entropy structures involving multiplicative couplings}}},
doi = {{10.1515/ans-2022-0004}},
volume = {{22}},
year = {{2022}},
}
@article{63305,
abstract = {{AbstractA no-flux initial-boundary value problem for the doubly degenrate parabolic system $$\begin{aligned} \left\{ \begin{array}{l} u_t = \nabla \cdot \big ( uv\nabla u\big ) + \ell uv, \\ v_t = \Delta v - uv, \end{array} \right. \qquad \qquad (\star ) \end{aligned}$$
u
t
=
∇
·
(
u
v
∇
u
)
+
ℓ
u
v
,
v
t
=
Δ
v
-
u
v
,
(
⋆
)
is considered in a smoothly bounded convex domain $$\Omega \subset \mathbb {R}^n$$
Ω
⊂
R
n
, with $$n\ge 1$$
n
≥
1
and $$\ell \ge 0$$
ℓ
≥
0
. The first of the main results asserts that for nonnegative initial data $$(u_0,v_0)\in (L^\infty (\Omega ))^2$$
(
u
0
,
v
0
)
∈
(
L
∞
(
Ω
)
)
2
with $$u_0\not \equiv 0$$
u
0
≢
0
, $$v_0\not \equiv 0$$
v
0
≢
0
and $$\sqrt{v_0}\in W^{1,2}(\Omega )$$
v
0
∈
W
1
,
2
(
Ω
)
, there exists a global weak solution (u, v) which, inter alia, belongs to $$C^0(\overline{\Omega }\times (0,\infty )) \times C^{2,1}(\overline{\Omega }\times (0,\infty ))$$
C
0
(
Ω
¯
×
(
0
,
∞
)
)
×
C
2
,
1
(
Ω
¯
×
(
0
,
∞
)
)
and satisfies $$\sup _{t>0} \Vert u(\cdot ,t)\Vert _{L^p(\Omega )}<\infty $$
sup
t
>
0
‖
u
(
·
,
t
)
‖
L
p
(
Ω
)
<
∞
for all $$p\in [1,p_0)$$
p
∈
[
1
,
p
0
)
with $$p_0:=\frac{n}{(n-2)_+}$$
p
0
:
=
n
(
n
-
2
)
+
. It is next seen that for each of these solutions one can find $$u_\infty \in \bigcap _{p\in [1,p_0)} L^p(\Omega )$$
u
∞
∈
⋂
p
∈
[
1
,
p
0
)
L
p
(
Ω
)
such that, within an appropriate topological setting, $$(u(\cdot ,t),v(\cdot ,t))$$
(
u
(
·
,
t
)
,
v
(
·
,
t
)
)
approaches the equilibrium $$(u_\infty ,0)$$
(
u
∞
,
0
)
in the large time limit. Finally, in the case $$n\le 5$$
n
≤
5
a result ensuring a certain stability property of any member in the uncountably large family of steady states $$(u_0,0)$$
(
u
0
,
0
)
, with arbitrary and suitably regular $$u_0:\Omega \rightarrow [0,\infty )$$
u
0
:
Ω
→
[
0
,
∞
)
, is derived. This provides some rigorous evidence for the appropriateness of ($$\star $$
⋆
) to model the emergence of a strikingly large variety of stable structures observed in experiments on bacterial motion in nutrient-poor environments. Essential parts of the analysis rely on the use of an apparently novel class of functional inequalities to suitably cope with the doubly degenerate diffusion mechanism in ($$\star $$
⋆
).}},
author = {{Winkler, Michael}},
issn = {{0944-2669}},
journal = {{Calculus of Variations and Partial Differential Equations}},
number = {{3}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Stabilization of arbitrary structures in a doubly degenerate reaction-diffusion system modeling bacterial motion on a nutrient-poor agar}}},
doi = {{10.1007/s00526-021-02168-2}},
volume = {{61}},
year = {{2022}},
}
@article{63311,
abstract = {{AbstractThe Cauchy problem in $$\mathbb {R}^n$$
R
n
, $$n\ge 1$$
n
≥
1
, for the degenerate parabolic equation $$\begin{aligned} u_t=u^p \Delta u \qquad \qquad (\star ) \end{aligned}$$
u
t
=
u
p
Δ
u
(
⋆
)
is considered for $$p\ge 1$$
p
≥
1
. It is shown that given any positive $$f\in C^0([0,\infty ))$$
f
∈
C
0
(
[
0
,
∞
)
)
and $$g\in C^0([0,\infty ))$$
g
∈
C
0
(
[
0
,
∞
)
)
satisfying $$\begin{aligned} f(t)\rightarrow + \infty \quad \text{ and } \quad g(t)\rightarrow 0 \qquad \text{ as } t\rightarrow \infty , \end{aligned}$$
f
(
t
)
→
+
∞
and
g
(
t
)
→
0
as
t
→
∞
,
one can find positive and radially symmetric continuous initial data with the property that the initial value problem for ($$\star $$
⋆
) admits a positive classical solution such that $$\begin{aligned} t^\frac{1}{p} \Vert u(\cdot ,t)\Vert _{L^\infty (\mathbb {R}^n)} \rightarrow \infty \qquad \text{ and } \qquad \Vert u(\cdot ,t)\Vert _{L^\infty (\mathbb {R}^n)} \rightarrow 0 \qquad \text{ as } t\rightarrow \infty , \end{aligned}$$
t
1
p
‖
u
(
·
,
t
)
‖
L
∞
(
R
n
)
→
∞
and
‖
u
(
·
,
t
)
‖
L
∞
(
R
n
)
→
0
as
t
→
∞
,
but that $$\begin{aligned} \liminf _{t\rightarrow \infty } \frac{t^\frac{1}{p} \Vert u(\cdot ,t)\Vert _{L^\infty (\mathbb {R}^n)}}{f(t)} =0 \end{aligned}$$
lim inf
t
→
∞
t
1
p
‖
u
(
·
,
t
)
‖
L
∞
(
R
n
)
f
(
t
)
=
0
and $$\begin{aligned} \limsup _{t\rightarrow \infty } \frac{\Vert u(\cdot ,t)\Vert _{L^\infty (\mathbb {R}^n)}}{g(t)} =\infty . \end{aligned}$$
lim sup
t
→
∞
‖
u
(
·
,
t
)
‖
L
∞
(
R
n
)
g
(
t
)
=
∞
.
}},
author = {{Winkler, Michael}},
issn = {{2662-2963}},
journal = {{Partial Differential Equations and Applications}},
number = {{4}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Oscillatory decay in a degenerate parabolic equation}}},
doi = {{10.1007/s42985-022-00186-z}},
volume = {{3}},
year = {{2022}},
}
@article{63312,
abstract = {{<p style='text-indent:20px;'>The chemotaxis system</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{array}{l}\left\{ \begin{array}{l} u_t = \nabla \cdot \big( D(u) \nabla u \big) - \nabla \cdot \big( uS(x, u, v)\cdot \nabla v\big), \\ v_t = \Delta v -uv, \end{array} \right. \end{array} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>is considered in a bounded domain <inline-formula><tex-math id="M1">\begin{document}$ \Omega\subset \mathbb{R}^n $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ n\ge 2 $\end{document}</tex-math></inline-formula>, with smooth boundary.</p><p style='text-indent:20px;'>It is shown that if <inline-formula><tex-math id="M3">\begin{document}$ D: [0, \infty) \to [0, \infty) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ S: \overline{\Omega}\times [0, \infty)\times (0, \infty)\to \mathbb{R}^{n\times n} $\end{document}</tex-math></inline-formula> are suitably smooth functions satisfying</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE2"> \begin{document}$ \begin{array}{l}D(u) \ge k_D u^{m-1} \qquad {\rm{for\; all}}\; u\ge 0 \end{array} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>and</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE3"> \begin{document}$ \begin{array}{l}|S(x, u, v)| \le \frac{S_0(v)}{v^\alpha} \qquad {\rm{for\; all}}\; (x, u, v)\; \in \Omega\times (0, \infty)^2 \end{array} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>with some</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE4"> \begin{document}$ \begin{array}{l}m>\frac{3n-2}{2n} \qquad {\rm{and}}\;\alpha\in [0, 1), \end{array} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>and with some <inline-formula><tex-math id="M5">\begin{document}$ k_D>0 $\end{document}</tex-math></inline-formula> and nondecreasing <inline-formula><tex-math id="M6">\begin{document}$ S_0: (0, \infty)\to (0, \infty) $\end{document}</tex-math></inline-formula>, then for all suitably regular initial data a corresponding no-flux type initial-boundary value problem admits a global bounded weak solution which actually is smooth and classical if <inline-formula><tex-math id="M7">\begin{document}$ D(0)>0 $\end{document}</tex-math></inline-formula>.</p>}},
author = {{Winkler, Michael}},
issn = {{1531-3492}},
journal = {{Discrete and Continuous Dynamical Systems - B}},
number = {{11}},
publisher = {{American Institute of Mathematical Sciences (AIMS)}},
title = {{{Approaching logarithmic singularities in quasilinear chemotaxis-consumption systems with signal-dependent sensitivities}}},
doi = {{10.3934/dcdsb.2022009}},
volume = {{27}},
year = {{2022}},
}
@article{63309,
abstract = {{AbstractThis manuscript is concerned with the problem of efficiently estimating chemotactic gradients, as forming a ubiquitous issue of key importance in virtually any proof of boundedness features in Keller–Segel type systems. A strategy is proposed which at its core relies on bounds for such quantities, conditional in the sense of involving certain Lebesgue norms of solution components that explicitly influence the signal evolution.Applications of this procedure firstly provide apparently novel boundedness results for two particular classes chemotaxis systems, and apart from that are shown to significantly condense proofs for basically well‐known statements on boundedness in two further Keller–Segel type problems.}},
author = {{Winkler, Michael}},
issn = {{0025-584X}},
journal = {{Mathematische Nachrichten}},
number = {{9}},
pages = {{1840--1862}},
publisher = {{Wiley}},
title = {{{A unifying approach toward boundedness in Keller–Segel type cross‐diffusion systems via conditional L∞$L^\infty$ estimates for taxis gradients}}},
doi = {{10.1002/mana.202000403}},
volume = {{295}},
year = {{2022}},
}
@article{63306,
author = {{Winkler, Michael}},
issn = {{0022-2518}},
journal = {{Indiana University Mathematics Journal}},
number = {{4}},
pages = {{1437--1465}},
publisher = {{Indiana University Mathematics Journal}},
title = {{{A critical blow-up exponent for flux limiation in a Keller-Segel system}}},
doi = {{10.1512/iumj.2022.71.9042}},
volume = {{71}},
year = {{2022}},
}
@article{63284,
abstract = {{ A no-flux initial-boundary value problem for the cross-diffusion system [Formula: see text] is considered in smoothly bounded domains [Formula: see text] with [Formula: see text]. It is shown that whenever [Formula: see text] is positive on [Formula: see text] and such that [Formula: see text] for some [Formula: see text], for all suitably regular positive initial data a global very weak solution, particularly preserving mass in its first component, can be constructed. This extends previous results which either concentrate on non-degenerate analogs, or are restricted to the special case [Formula: see text]. To appropriately cope with the considerably stronger cross-degeneracies thus allowed through [Formula: see text] when [Formula: see text] is large, in its core part the analysis relies on the use of the Moser–Trudinger inequality in controlling the respective diffusion rates [Formula: see text] from below. }},
author = {{Winkler, Michael}},
issn = {{1664-3607}},
journal = {{Bulletin of Mathematical Sciences}},
number = {{02}},
publisher = {{World Scientific Pub Co Pte Ltd}},
title = {{{Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model}}},
doi = {{10.1142/s1664360722500126}},
volume = {{13}},
year = {{2022}},
}
@article{63286,
abstract = {{ The chemotaxis system [Formula: see text] is considered in a ball [Formula: see text]. It is shown that if [Formula: see text] suitably generalizes the prototype given by [Formula: see text] with some [Formula: see text], and if diffusion is suitably weak in the sense that [Formula: see text] is such that there exist [Formula: see text] and [Formula: see text] fulfilling [Formula: see text] then for appropriate choices of sufficiently concentrated initial data, an associated no-flux initial-boundary value problem admits a global classical solution [Formula: see text] which blows up in infinite time and satisfies [Formula: see text] A major part of the proof is based on a comparison argument involving explicitly constructed subsolutions to a scalar parabolic problem satisfied by mass accumulation functions corresponding to solutions of ( ⋆ ). }},
author = {{Winkler, Michael}},
issn = {{0921-7134}},
journal = {{Asymptotic Analysis}},
number = {{1}},
pages = {{33--57}},
publisher = {{SAGE Publications}},
title = {{{Exponential grow-up rates in a quasilinear Keller–Segel system}}},
doi = {{10.3233/asy-221765}},
volume = {{131}},
year = {{2022}},
}
@article{63293,
abstract = {{<p style='text-indent:20px;'>The Cauchy problem in <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{R}^3 $\end{document}</tex-math></inline-formula> for the chemotaxis-Navier–Stokes system</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{eqnarray*} \left\{ \begin{array}{l} n_t + u\cdot\nabla n = \Delta n - \nabla \cdot (n\nabla c), \\ c_t + u\cdot\nabla c = \Delta c - nc, \\ u_t + (u\cdot\nabla) u = \Delta u + \nabla P + n\nabla\phi, \qquad \nabla \cdot u = 0, \ \end{array} \right. \end{eqnarray*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>is considered. Under suitable conditions on the initial data <inline-formula><tex-math id="M3">\begin{document}$ (n_0, c_0, u_0) $\end{document}</tex-math></inline-formula>, with regard to the crucial first component requiring that <inline-formula><tex-math id="M4">\begin{document}$ n_0\in L^1( \mathbb{R}^3) $\end{document}</tex-math></inline-formula> be nonnegative and such that <inline-formula><tex-math id="M5">\begin{document}$ (n_0+1)\ln (n_0+1) \in L^1( \mathbb{R}^3) $\end{document}</tex-math></inline-formula>, a globally defined weak solution with <inline-formula><tex-math id="M6">\begin{document}$ (n, c, u)|_{t = 0} = (n_0, c_0, u_0) $\end{document}</tex-math></inline-formula> is constructed. Apart from that, assuming that moreover <inline-formula><tex-math id="M7">\begin{document}$ \int_{ \mathbb{R}^3} n_0(x) \ln (1+|x|^2) dx $\end{document}</tex-math></inline-formula> is finite, it is shown that a weak solution exists which enjoys further regularity features and preserves mass in an appropriate sense.</p>}},
author = {{Kang, Kyungkeun and Lee, Jihoon and Winkler, Michael}},
issn = {{1078-0947}},
journal = {{Discrete and Continuous Dynamical Systems}},
number = {{11}},
publisher = {{American Institute of Mathematical Sciences (AIMS)}},
title = {{{Global weak solutions to a chemotaxis-Navier-Stokes system in $ \mathbb{R}^3 $}}},
doi = {{10.3934/dcds.2022091}},
volume = {{42}},
year = {{2022}},
}