Global boundedness of solutions to a chemotaxis-fluid system with singular sensitivity and logistic source

Guoqiang Ren; Bin Liu

doi:10.3934/cpaa.2020170

Article Contents

2020, Volume 19, Issue 7: 3843-3883. Doi: 10.3934/cpaa.2020170

This issue Previous Article Algebraic structure of the $ L_2 $ analytic Fourier–Feynman transform associated with Gaussian paths on Wiener space Next Article Blow-up for semilinear wave equations with time-dependent damping in an exterior domain

Global boundedness of solutions to a chemotaxis-fluid system with singular sensitivity and logistic source

Guoqiang Ren^1,2,3, and
Bin Liu^1,2, ,

1.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
2.
Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China
3.
Institute of Artificial Intelligence, Huazhong University of Science and Technology, Wuhan 430074, China

^* Corresponding author
^* Corresponding author

Received: January 2020

Revised: February 2020

Published: April 2020

The authors were supported by NSFC grant 11971185

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Abstract

In this paper, we investigate the chemotaxis-fluid system with singular sensitivity and logistic source in bounded convex domain with smooth boundary. We present the global existence of very weak solutions under appropriate regularity assumptions on the initial data. Then, we show that system possesses a global bounded classical solution. Finally, we present a unique globally bounded classical solution for a fluid-free system. In addition, the asymptotic behavior of the solutions is studied, and our results generalize and improve some well-known results in the literature, and partially results are new.

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Mathematics Subject Classification: Primary: 35D30, 35K45, 35A01, 35Q92, 92C17.

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