@article{63254,
abstract = {{AbstractThe chemotaxis-Navier–Stokes system $$\begin{aligned} \left\{ \begin{array}{rcl} n_t+u\cdot \nabla n & =& \Delta \big (n c^{-\alpha } \big ), \\ c_t+ u\cdot \nabla c & =& \Delta c -nc,\\ u_t + (u\cdot \nabla ) u & =& \Delta u+\nabla P + n\nabla \Phi , \qquad \nabla \cdot u=0, \end{array} \right. \end{aligned}$$
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modelling the behavior of aerobic bacteria in a fluid drop, is considered in a smoothly bounded domain $$\Omega \subset \mathbb R^2$$
Ω
⊂
R
2
. For all $$\alpha > 0$$
α
>
0
and all sufficiently regular $$\Phi $$
Φ
, 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 u at a point in the proof when knowledge about n is essentially limited to the observation that the mass is conserved. To overcome this problem, we also prove new uniform-in-time $$L^p$$
L
p
estimates for solutions to the inhomogeneous Navier–Stokes equations merely depending on the space-time $$L^2$$
L
2
norm of the force term raised to an arbitrary small power.}},
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{34669,
author = {{Black, Tobias}},
issn = {{1422-6928}},
journal = {{Journal of Mathematical Fluid Mechanics}},
keywords = {{Applied Mathematics, Computational Mathematics, Condensed Matter Physics, Mathematical Physics}},
number = {{1}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System}}},
doi = {{10.1007/s00021-019-0464-z}},
volume = {{22}},
year = {{2019}},
}
@article{63375,
author = {{Winkler, Michael}},
issn = {{1422-6928}},
journal = {{Journal of Mathematical Fluid Mechanics}},
number = {{4}},
pages = {{1889--1909}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Does Fluid Interaction Affect Regularity in the Three-Dimensional Keller–Segel System with Saturated Sensitivity?}}},
doi = {{10.1007/s00021-018-0395-0}},
volume = {{20}},
year = {{2018}},
}