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

Thierry Gallay, Yasunori Maekawa

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)973-991
Number of pages19
JournalAnalysis and PDE
Volume6
Issue number4
DOIs
Publication statusPublished - 2013

Keywords

  • Exterior domains
  • Long-time asymptotics
  • Navier-Stokes equations
  • Oseen vortices

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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