Article
| Title: | Global weak solutions to a 3D self-consistent chemotaxis-Stokes system with nonlinear resource consumption (English) |
| Author: | Ri, Kwang-Ok |
| Author: | Kim, Yong-Ho |
| Author: | Paek, Jong-Chol |
| Author: | Hong, Song-Chol |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 70 |
| Issue: | 5 |
| Year: | 2025 |
| Pages: | 695-709 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We study the self-consistent chemotaxis-fluid system with nonlinear resource consumption $$ \begin {cases} n_{t}+u\cdot \nabla n=\Delta n^m -\nabla \cdot (n \nabla c)+\nabla \cdot (n\nabla \phi ), & x\in \Omega ,\ t>0, \\ c_{t}+u\cdot \nabla c=\Delta c-n^\alpha c, & x\in \Omega ,\ t>0, \\ u_t+ \nabla P=\Delta u-n\nabla \phi +n \nabla c,& x\in \Omega ,\ t>0,\\ \nabla \cdot u=0,& x\in \Omega ,\ t>0,\\ \end {cases} $$ under no-flux boundary conditions in a bounded domain $\Omega \subset \mathbb {R}^3$ with smooth boundary. It is proved that this system possesses a global weak solution provided $m>1$ and $\alpha > \frac {4}{3}$. (English) |
| Keyword: | chemotaxis |
| Keyword: | self-consistent |
| Keyword: | weak solution |
| Keyword: | consumption |
| MSC: | 35K92 |
| MSC: | 35Q35 |
| MSC: | 35Q92 |
| MSC: | 92C17 |
| DOI: | 10.21136/AM.2025.0041-25 |
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| Date available: | 2025-11-07T17:58:54Z |
| Last updated: | 2025-11-16 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153155 |
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