Boundedness in a three-dimensional chemotaxis-Stokes system with tensor-valued sensitivity

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• 作者：Yulan Wang ; ^{wangyulan-math@163.com" class="auth_mail" title="E-mail the corresponding author} ; Fengqin Pang ; Huifang Li
• 关键词：Chemotaxis-Stokes system ; Boundedness ; Stabilization ; Tensor-valued sensitivity
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：71
• 期：3
• 页码：712-722
• 全文大小：397 K

文摘

This paper is concerned with the chemotaxis-Stokes system under no-flux boundary conditions in a bounded domain Ω⊂R³$\Omega \subset {\mathbb{R}}^3$ with smooth boundary. Here S$S$ is a matrix-valued sensitivity satisfying $\left|S(x,n,c)\right|<\tilde{C}{(1+n)}^{-\alpha }$ with some $\tilde{C}>0$ and α>0$\alpha >0$. We shall first establish the boundedness of (⋆$\star$) through a series of a priori estimate, and then propose the stabilization of the classical solution. This result gives a definite answer to the conjecture in Remark 1.2 by Y. Wang and X. Cao (2015) and extends the main result of that paper.