Article
| Title: | Asymptotic behavior of small-data solutions to a Keller-Segel-Navier-Stokes system with indirect signal production (English) |
| Author: | Yang, Lu |
| Author: | Liu, Xi |
| Author: | Hou, Zhibo |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 1 |
| Year: | 2023 |
| Pages: | 49-70 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We consider the Keller-Segel-Navier-Stokes system $$ \begin{cases} n_t+{\bf u}\cdot \nabla n =\Delta n - \nabla \cdot (n\nabla v ),& x\in \Omega ,\ t>0,\\ v_t +{\bf u}\cdot \nabla v=\Delta v -v+w, &x\in \Omega ,\ t>0,\\ w_t+{\bf u}\cdot \nabla w=\Delta w -w+n, &x\in \Omega ,\ t>0,\\ {\bf {u}}_t + ({\bf {u}}\cdot \nabla ){\bf {u}} = \Delta {\bf {u}} + \nabla P + n\nabla \phi ,\ \nabla \cdot {\bf u}=0, &x\in \Omega ,\ t>0, \end{cases} $$ which is considered in bounded domain $\Omega \subset \mathbb {R}^N$ $(N \in \{2,3\})$ with smooth boundary, where $\phi \in C^{1+\delta }(\overline \Omega )$ with $\delta \in (0,1)$. We show that if the initial data $\|n_0\|_{L^{{N}/{2}}(\Omega )}$, $\|\nabla v_0\|_{L^N(\Omega )}$, $\|\nabla w_0\|_{L^N(\Omega )}$ and $\|{\bf u}_0\|_{L^N(\Omega )}$ is small enough, an associated initial-boundary value problem possesses a global classical solution which decays to the constant state $({\bar n}_0,{\bar n}_0,{\bar n}_0,0)$ exponentially with ${\bar n}_0:=(1/|\Omega |)\int _{\Omega }n_0(x){\rm d}x$. (English) |
| Keyword: | Keller-Segel-Navier-Stokes |
| Keyword: | global solution |
| Keyword: | decay estimate |
| Keyword: | indirect process |
| MSC: | 35B35 |
| MSC: | 35B40 |
| MSC: | 35K55 |
| MSC: | 35Q35 |
| MSC: | 92C17 |
| idZBL: | Zbl 07655755 |
| idMR: | MR4541089 |
| DOI: | 10.21136/CMJ.2022.0399-21 |
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| Date available: | 2023-02-03T11:07:34Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151504 |
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