NDLI: Global classical small-data solutions for a three-dimensional chemotaxis Navier–Stokes system involving matrix-valued sensitivities

Content Provider	SpringerLink
Author	Cao, Xinru Lankeit, Johannes
Copyright Year	2016
Abstract	The coupled chemotaxis fluid system $$\begin{aligned} \left\{ \begin{array}{lll} n_t=\Delta n-\nabla \cdot (n S(x,n,c)\cdot \nabla c)-u\cdot \nabla n, &{}\quad (x,t)\in \Omega \times (0,T),\\ c_t=\Delta c-nc-u\cdot \nabla c, &{}\quad (x,t)\in \Omega \times (0,T),\\ u_t=\Delta u-(u\cdot \nabla )u+\nabla P+n\nabla \Phi ,\quad \nabla \cdot u=0, &{}\quad (x,t)\in \Omega \times (0,T),\\ \nabla c\cdot \nu =(\nabla n-nS(x,n,c)\cdot \nabla c)\cdot \nu =0, \;\; u=0,&{}\quad (x,t)\in \partial \Omega \times (0,T),\\ n(x,0)=n_{0}(x),\quad c(x,0)=c_{0}(x),\quad u(x,0)=u_0(x), &{}\quad x\in \Omega , \end{array} \right. \end{aligned}$$ where $$S\in (C^2({\overline{\Omega }}\times [0,\infty )^2))^{N\times N}$$ , is considered in a bounded domain $$\Omega \subset \mathbb {R}^N$$ , $$N\in \{2,3\}$$ , with smooth boundary. We show that it has global classical solutions if the initial data satisfy certain smallness conditions and give decay properties of these solutions.
Ending Page	39
Page Count	39
Starting Page	1
File Format	PDF
ISSN	09442669
e-ISSN	14320835
Journal	Calculus of Variations and Partial Differential Equations
Issue Number	4
Volume Number	55
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-08-01
Publisher Place	Berlin, Heidelberg
Access Restriction	Subscribed
Subject Keyword	Stability Systems Theory, Control Calculus of Variations and Optimal Control; Optimization PDEs in connection with fluid mechanics Analysis Theoretical, Mathematical and Computational Physics Cell movement (chemotaxis, etc.) Nonlinear parabolic equations Asymptotic behavior of solutions
Content Type	Text
Resource Type	Article
Subject	Analysis Applied Mathematics

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