Stabilization of the chemotaxis-Navier-Stokes equations: Maximal regularity approach

[摘要] Consider the chemotaxis-Navier-Stokes equations in a bounded smooth domain Omega C R-d for d >= 3. We show that any solution starting close to an equilibrium exists globally and converges exponentially fast to the equilibrium as time tends to infinity, provided that the initial density n(0) of amoebae satisfies integral(Omega) n(0) dx < 2 vertical bar Omega vertical bar, where vertical bar Omega vertical bar stands for the Lebesgue measure of Omega. First, we prove the existence of a local strong solution for large initial data. Then, the global existence result is obtained assuming that the initial data are close to the equilibrium in their natural norm. In particular, we show the strong solution in the maximal L-p - L-q-regularity class with (p, q) is an element of (2, infinity) x (d, infinity) satisfying 2/p+d/q < 1. Furthermore, the solution is real analytic in space and time. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-15

[关键词] Chemotaxis-Navier-Stokes equations;Well-posedness;Stabilization;Maximal regularity