Global boundedness of classical solutions to a Keller-Segel-Navier-Stokes system involving saturated sensitivity and indirect signal production in two dimensions
| Title: | Global boundedness of classical solutions to a Keller-Segel-Navier-Stokes system involving saturated sensitivity and indirect signal production in two dimensions |
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| Authors: | Kai Gao |
| Source: | Electronic Research Archive, Vol 31, Iss 3, Pp 1710-1736 (2023) |
| Publisher Information: | AIMS Press, 2023. |
| Publication Year: | 2023 |
| Collection: | LCC:Mathematics LCC:Applied mathematics. Quantitative methods |
| Subject Terms: | keller-segel-navier-stokes system, tensor-valued sensitivity, indirect signal production, classical solution, global boundedness, Mathematics, QA1-939, Applied mathematics. Quantitative methods, T57-57.97 |
| More Details: | This paper is concerned with the following Keller–Segel–Navier–Stokes system with indirect signal production and tensor-valued sensitivity: $ \left\{\begin{array}{*5{lllll }} n_{t}+u \cdot \nabla n=\Delta n-\nabla \cdot(n S(x,n,v,w) \nabla v), \quad &x \in \Omega, t>0, \\ v_{t}+u \cdot \nabla v=\Delta v-v+w, \quad &x \in \Omega, t>0, \\ w_{t}+u \cdot \nabla w=\Delta w-w+n, \quad &x \in \Omega, t>0, \\ u_{t}+\kappa(u \cdot \nabla) u+\nabla P=\Delta u+n \nabla \phi, \quad &x \in \Omega, t>0, \\ \nabla \cdot u=0, \quad &x \in \Omega, t>0, \end{array}\right. \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (♡)$ in a bounded domain $ \Omega\subset \mathbb{R}^2 $ with smooth boundary, where $ \kappa \in \mathbb{R} $, $ \phi \in W^{2, \infty}(\Omega) $, and $ S $ is a given function with values in $ \mathbb{R}^{2\times2} $ which satisfies $ |S(x, v, w, u)|\leq C_{S}(n+1)^{-\alpha} $ with $ C_{S} > 0 $. If $ \alpha > 0 $, then for any sufficiently smooth initial data, there exists a globally classical solution which is bounded for the corresponding initial-boundary value problem of system (♡). |
| Document Type: | article |
| File Description: | electronic resource |
| Language: | English |
| ISSN: | 2688-1594 |
| Relation: | https://doaj.org/toc/2688-1594 |
| DOI: | 10.3934/era.2023089?viewType=HTML |
| DOI: | 10.3934/era.2023089 |
| Access URL: | https://doaj.org/article/a5d1a32ae7f24baa89b64497d75d23bd |
| Accession Number: | edsdoj.5d1a32ae7f24baa89b64497d75d23bd |
| Database: | Directory of Open Access Journals |
| ISSN: | 26881594 |
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| DOI: | 10.3934/era.2023089?viewType=HTML |
| Published in: | Electronic Research Archive |
| Language: | English |