Global classical solutions in chemotaxis(-Navier)-Stokes system with rotational flux term. (English) Zbl 1352.35092
The Navier-Stokes equations coupled with the Keller-Segel system with rather general matrix-valued sensitivity function are considered in two space dimensions, and the Stokes-Keller-Segel system in three dimensions. Under smallness assumptions on the initial concentration of the chemoattractant, the global in time existence of classical solutions is proved together with some stabilization estimates.
Reviewer: Piotr Biler (Wrocław)
MSC:
| 35Q30 | Navier-Stokes equations |
| 92C17 | Cell movement (chemotaxis, etc.) |
| 35K45 | Initial value problems for second-order parabolic systems |
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