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Periodic pattern formation in the coupled chemotaxis-(Navier–)Stokes system with mixed nonhomogeneous boundary conditions

Part of: Equations and systems of special type Physiological, cellular and medical topics

Published online by Cambridge University Press:  04 November 2019

Chunhua Jin
Chunhua Jin*
Affiliation:
School of Mathematical Sciences, Normal University, Guangzhou510631, South China (jinchhua@126.com)
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Abstract

We consider the coupled chemotaxis-fluid model for periodic pattern formation on two- and three-dimensional domains with mixed nonhomogeneous boundary value conditions, and prove the existence of nontrivial time periodic solutions. It is worth noticing that this system admits more than one periodic solution. In fact, it is not difficult to verify that (0, c, 0, 0) is a time periodic solution. Our purpose is to obtain a time periodic solution with nonconstant bacterial density.

Keywords

chemotaxis-fluid systemmixed boundarytime periodic patternclassical solution

MSC classification

Primary: 92C17: Cell movement (chemotaxis, etc.) 92C15: Developmental biology, pattern formation 35M10: Equations of mixed type
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 6 , December 2020 , pp. 3121 - 3152
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Copyright
Copyright © 2019 The Royal Society of Edinburgh

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