Global existence and boundedness in a Keller-Segel-(Navier-)Stokes system with signal-dependent sensitivity

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• 作者：Ji Liu^a ; Yifu Wang^a ; ^b ; ^{wangyifu@bit.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Keller&ndash ; Segel ; Navier&ndash ; Stokes ; Stokes ; Boundedness ; Global existence
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：447
• 期：1
• 页码：499-528
• 全文大小：564 K

文摘

In this paper, we consider the following Keller–Segel(–Navier)–Stokes system where Ω⊂R^N (N=2,3)$\mathrm{\Omega }\subset {\mathbb{R}}^N(N=2,3)$ is a bounded domain with smooth boundary ∂Ω, κ∈R$\partial \mathrm{\Omega },\kappa \in \mathbb{R}$ and χ(c)$\chi (c)$ is assumed to generalize the prototype It is proved that i) for κ≠0$\kappa \ne 0$ and N=2$N=2$ or κ=0$\kappa =0$ and N∈{2,3}$N\in \{2,3\}$, the corresponding initial–boundary problem admits a unique global classical solution which is bounded; ii) for κ≠0$\kappa \ne 0$ and 4f1c460f83c1c3027d833f8f6a67007" title="Click to view the MathML source">N=3$N=3$, the corresponding initial–boundary problem possesses at least one global weak solution.