# Stabilization of the chemotaxis–Navier–Stokes equations: Maximal regularity approach

## 抄録

Consider the chemotaxis–Navier–Stokes equations in a bounded smooth domain Ω⊂Rd 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 n0 of amoebae satisfies ∫Ωn0dx<2|Ω|, where |Ω| stands for the Lebesgue measure of Ω. 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 Lp−Lq-regularity class with (p,q)∈(2,∞)×(d,∞) satisfying 2/p+d/q<1. Furthermore, the solution is real analytic in space and time.

本文言語 English 125422 Journal of Mathematical Analysis and Applications 504 2 https://doi.org/10.1016/j.jmaa.2021.125422 Published - 2021 12 15

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• 応用数学

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