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.
Bin Liu, Guoqiang Ren
Huazhong University of Science and Technology; Huazhong University of Science and Technology
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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