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

研究成果: Article査読

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
論文番号125422
ジャーナルJournal of Mathematical Analysis and Applications
504
2
DOI
出版ステータスPublished - 2021 12 15

ASJC Scopus subject areas

  • 分析
  • 応用数学

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