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Global classical solution to the chemotaxis-Navier-Stokes system with some realistic boundary conditions

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

Published online by Cambridge University Press:  02 March 2023

Chunhua Jin
Chunhua Jin*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China (jinchhua@126.com)
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Abstract

In this paper, we consider the chemotaxis-Navier-Stokes model with realistic boundary conditions matching the experiments of Hillesdon, Kessler et al. in a two-dimensional periodic strip domain. For the lower boundary, we impose the usual homogeneous Neumann-Neumann-Dirichlet boundary condition. While, for the upper boundary, since it is open to the atmosphere, we consider three kinds of different mixed non-homogeneous boundary conditions, that is, (i) Neumann-Dirichlet-Navier slip boundary condition; (ii) Zero flux-Dirichlet-Navier slip boundary condition; (iii) Zero flux-Robin-Navier slip boundary condition. For boundary conditions (i) and (iii), the existence and uniqueness of global classical solutions for any initial data and any large chemotactic sensitivity coefficient is established, and for boundary condition (ii), the existence and uniqueness of global classical solutions for any initial data and small chemotactic sensitivity coefficient is proved.

Keywords

Chemotaxis-Navier-Stokes systemmixed nonhomogeneous boundary conditionsglobal classical solutionuniqueness

MSC classification

Primary: 35M33: Initial-boundary value problems for systems of mixed type
Secondary: 35A09: Classical solutions 92C17: Cell movement (chemotaxis, etc.)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 154 , Issue 2 , April 2024 , pp. 445 - 482
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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