Long-Time asymptotics for two-dimensional exterior flows with small circulation at infinity

Thierry Gallay, Yasunori Maekawa

研究成果: Article査読

7 被引用数 (Scopus)

抄録

We consider the incompressible Navier-Stokes equations in a two-dimensional exterior domain Ω, with no-slip boundary conditions. Our initial data are of the form u0 = αΘ0 + v0, where Θ0 is the Oseen vortex with unit circulation at infinity and v0 is a solenoidal perturbation belonging to L2.(Ω)2 ∩ Lq.(Ω)2 for some q ε (1,2). If α ε ℝ is sufficiently small, we show that the solution behaves asymptotically in time like the self-similar Oseen vortex with circulation α. This is a global stability result, in the sense that the perturbation v0 can be arbitrarily large, and our smallness assumption on the circulation α is independent of the domain Ω.

本文言語English
ページ(範囲)973-991
ページ数19
ジャーナルAnalysis and PDE
6
4
DOI
出版ステータスPublished - 2013

ASJC Scopus subject areas

  • 分析
  • 数値解析
  • 応用数学

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