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

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 L(Ω) ∩Lq(Ω)2 for some q ∈ (1, 2). If α ∈ 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.

Cite this paper

@inproceedings{Gallay2017LongtimeAF, title={Long-time asymptotics for two-dimensional exterior flows with small circulation at infinity}, author={Thierry Gallay and Yasunori Maekawa}, year={2017} }