English

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

Analysis of PDEs 2012-02-23 v1

Abstract

We consider the incompressible Navier-Stokes equations in a two-dimensional exterior domain, with no-slip boundary conditions. We assume that the initial velocity is a finite-energy and L^q-summable perturbation of the Oseen vortex with circulation \alpha, where 1 < q < 2. If {\alpha} is sufficiently small, we show that the solution behaves asymptotically in time like the self-similar Oseen vortex with circulation \alpha. This is a global stability result, which holds for arbitrarily large perturbations of the Oseen vortex, and our smallness assumption on the circulation is independent of the domain under consideration.

Keywords

Cite

@article{arxiv.1202.4969,
  title  = {Long-time asymptotics for two-dimensional exterior flows with small circulation at infinity},
  author = {Thierry Gallay and Yasunori Maekawa},
  journal= {arXiv preprint arXiv:1202.4969},
  year   = {2012}
}

Comments

18 pages

R2 v1 2026-06-21T20:23:33.110Z