Boundedness and large time behavior in a three-dimensional\n chemotaxis-Stokes system with nonlinear diffusion and general sensitivity

2015/01/28 by Michael Winkler, Winkler, Michael · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #35K55 #35Q35 #35Q92 #92C17 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.1501.07059

openalex publication_date 2015/01/28 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We consider a chemotaxis-fluid system involving nonlinear cell diffusion of\nporous medium type, signal consumption by cells, and rather general, possibly\nmatrix-valued, chemotactic sensitivities. It is shown that if the corresponding\ndiffusion exponent m satisfies m>7/6, then for all reasonably regaular\ninitial data an associated initial-boundary value problem in smoothly bounded\nthree-dimensional domains possesses a globally defined weak solution which is\nbounded. Under a mild additional assumption on the signal consumption rate, it\nis moreover shown that any nontrivial of these solutions stabilizes toward a\nspatially homogeneous equilibrium in the large time limit.\n

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