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J. Korean Math. Soc. 2020; 57(1): 215-247

Online first article September 18, 2019      Printed January 1, 2020

https://doi.org/10.4134/JKMS.j190028

Copyright © The Korean Mathematical Society.

Global existence and asymptotic behavior in a three-dimensional two-species chemotaxis-Stokes system with tensor-valued sensitivity

Bin Liu, Guoqiang Ren

Huazhong University of Science and Technology; Huazhong University of Science and Technology

Abstract

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In this paper, we deal with a two-species chemotaxis-Stokes system with Lotka-Volterra competitive kinetics under homogeneous Neumann boundary conditions in a general three-dimensional bounded domain with smooth boundary. Under appropriate regularity assumptions on the initial data, by some $L^p$-estimate techniques, we show that the system possesses at least one global and bounded weak solution, in addition to discussing the asymptotic behavior of the solutions. Our results generalizes and improves partial previously known ones.

Keywords: Chemotaxis-Stokes, boundedness, asymptotic behavior, global existence

MSC numbers: 35D30, 35K46, 35A01, 35Q92, 35B35, 92C17

Supported by: This work was partially supported by NNSF of China (Grant No. 11971185).

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