Global existence and asymptotic behavior of classical solutions for a 3D two-species Keller-Segel-Stokes system with competitive kinetics. (English) Zbl 1442.35323
Summary: This paper deals with a two-species Keller-Segel-Stokes system with competitive kinetics under homogeneous Neumann boundary conditions in a bounded domain with smooth boundary. The main purpose of this paper is to obtain global existence and stabilization of classical solutions to the system in the 3-dimensional case under the smallness conditions for chemotactic interactions. To this end, this paper develops a maximal Sobolev regularity result for Stokes operator involving a time weighted function, which seems new in the existing literature (see Lemma 2.3 in this paper).
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35A09 | Classical solutions to PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 76Z05 | Physiological flows |
| 92C17 | Cell movement (chemotaxis, etc.) |
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