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Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement. (English) Zbl 1395.35038

Chemotaxis-Stokes systems with nonlinear diffusion are studied in three-dimensional domains. Construction of global in time solutions of the initial-boundary value problem is achieved by a combination of energy arguments with the maximal Sobolev regularity theory. These solutions tend to homogeneous steady states as time goes to infinity.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
35Q35 PDEs in connection with fluid mechanics
92C17 Cell movement (chemotaxis, etc.)
35K55 Nonlinear parabolic equations
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