Global existence and asymptotic behavior in a three-dimensional two-species chemotaxis-Stokes system with tensor-valued sensitivity
J. Korean Math. Soc. 2020 Vol. 57, No. 1, 215-247
https://doi.org/10.4134/JKMS.j190028
Published online January 1, 2020
Bin Liu, Guoqiang Ren
Huazhong University of Science and Technology; Huazhong University of Science and Technology
Abstract : 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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