Boundedness for a 3D chemotaxis–Stokes system with porous medium diffusion and tensor-valued chemotactic sensitivity

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• 作者：Yilong Wang ; Xie Li
• 关键词：Chemotaxis ; Stokes ; Porous medium diffusion ; Boundedness ; Global existence
• 刊名：Zeitschrift für angewandte Mathematik und Physik
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：68
• 期：2
• 全文大小：
• 刊物主题：Theoretical and Applied Mechanics; Mathematical Methods in Physics;
• 出版者：Springer International Publishing
• ISSN：1420-9039
• 卷排序：68

文摘

This paper deals with the following chemotaxis–Stokes system $$\begin{aligned} \left\{ \begin{array}{ll} n_t+u\cdot \nabla n=\Delta n^m-\nabla \cdot (nS(x,n,c)\cdot \nabla c), &{}\quad x\in \Omega ,\,\, t>0,\\ c_t+u\cdot \nabla c=\Delta c-nf(c),&{}\quad x\in \Omega , \,\,t>0,\\ u_t=\Delta u+\nabla P+n\nabla \phi ,&{}\quad x\in \Omega , \,\,t>0,\\ \nabla \cdot u=0,&{}\quad x\in \Omega , \,\,t>0\\ \end{array} \right. \end{aligned}$$under no-flux boundary conditions in a bounded domain \(\Omega \subset \mathbb {R}^{3}\) with smooth boundary, where \(m\ge 1\), \(\phi \in W^{1,\infty }(\Omega )\), f and S are given functions with values in \([0,\,\infty )\) and \(\mathbb {R}^{3\times 3}\), respectively. Here S satisfies \(|S(x,n,c)|<S_0(c)(1+n)^{-\alpha }\) with \(\alpha \ge 0\) and some nonnegative nondecreasing function \(S_0\). With the tensor-valued sensitivity S, this system does not possess energy-type functionals which seem to be available only when S is a scalar function. 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Anal. 46, 3078–3105 (2014)MathSciNetCrossRefMATHGoogle ScholarCopyright information© Springer International Publishing 2017Authors and AffiliationsYilong Wang1Xie Li2Email author1.School of SciencesSouthwest Petroleum UniversityChengduChina2.College of Mathematic and InformationChina West Normal UniversityNanchongChina About this article CrossMark Publisher Name Springer International Publishing Print ISSN 0044-2275 Online ISSN 1420-9039 About this journal Reprints and Permissions Article actions .buybox { margin: 16px 0 0; position: relative; } .buybox { font-family: Source Sans Pro, Helvetica, Arial, sans-serif; font-size: 14px; font-size: .875rem; } .buybox { zoom: 1; } .buybox:after, .buybox:before { content: ''; display: table; } .buybox:after { clear: both; } /*---------------------------------*/ .buybox .buybox__header { border: 1px solid #b3b3b3; border-bottom: 0; padding: 8px 12px; position: relative; background-color: #f2f2f2; } .buybox__header .buybox__login { font-family: Source Sans Pro, Helvetica, Arial, sans-serif; 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