Global existence and decay rates to a self-consistent chemotaxis-fluid system. (English) Zbl 1529.35529
A new Keller-Segel-(Navier-)Stokes system is considered in two and three space dimensions. The main novelty is the coupling term \(\chi(c)n\nabla c\) (a chemotactic force) in the evolution of fluid equations which makes the system self-consistent, and simultaneously more difficult in the analysis. Extensibility of classical solutions is studied, and a new entropy functional inequality is applied. Existence of global-in-time solutions and their decay rates are established.
Reviewer: Piotr Biler (Wrocław)
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 35Q35 | PDEs in connection with fluid mechanics |
| 35K55 | Nonlinear parabolic equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
Keywords:
chemotaxis-fluid system; self-consistent; global-in-time solutions; blow-up criterion; decay rateReferences:
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