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The convergence rate of the fast signal diffusion limit for a Keller–Segel–Stokes system with large initial data

Part of: Equations of mathematical physics and other areas of application Physiological, cellular and medical topics Parabolic equations and systems

Published online by Cambridge University Press:  23 December 2020

Min Li  and
Zhaoyin Xiang
Min Li
Affiliation:
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China (limin_pde@163.com; zxiang@uestc.edu.cn)
Zhaoyin Xiang
Affiliation:
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China (limin_pde@163.com; zxiang@uestc.edu.cn)
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Abstract

In this paper, we investigate the fast signal diffusion limit of solutions of the fully parabolic Keller–Segel–Stokes system to solution of the parabolic–elliptic-fluid counterpart in a two-dimensional or three-dimensional bounded domain with smooth boundary. Under the natural volume-filling assumption, we establish an algebraic convergence rate of the fast signal diffusion limit for general large initial data by developing a series of subtle bootstrap arguments for combinational functionals and using some maximal regularities. In our current setting, in particular, we can remove the restriction to asserting convergence only along some subsequence in Wang–Winkler and the second author (Cal. Var., 2019).

Keywords

Keller–Segel–Stokes systemlarge initial datafast signal diffusion limitconvergence rate

MSC classification

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35Q92: PDEs in connection with biology and other natural sciences 92C17: Cell movement (chemotaxis, etc.)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 6 , December 2021 , pp. 1972 - 2012
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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