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GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR IN A THREE-DIMENSIONAL TWO-SPECIES CHEMOTAXIS-STOKES SYSTEM WITH TENSOR-VALUED SENSITIVITY

  • Liu, Bin (School of Mathematics and Statistics Huazhong University of Science and Technology) ;
  • Ren, Guoqiang (School of Mathematics and Statistics Huazhong University of Science and Technology)
  • Received : 2019.01.09
  • Accepted : 2019.08.14
  • Published : 2019.12.30

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 Lp-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.

Acknowledgement

Supported by : NNSF of China

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