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.
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