Long-time asymptotics for two-dimensional exterior flows with small circulation at infinity
- 21 August 2013
- journal article
- research article
- Published by Mathematical Sciences Publishers in Analysis & PDE
- Vol. 6 (4) , 973-991
- https://doi.org/10.2140/apde.2013.6.973
Abstract
We consider the incompressible Navier-Stokes equations in a two-dimensional exterior domain Omega, with no-slip boundary conditions. Our initial data are of the form u(0) = alpha Theta(0) + v(0), where, Theta(0) is the Oseen vortex with unit circulation at infinity and v(0) is a solenoidal perturbation belonging to L-2(Omega)(2) boolean AND L-q(Omega)(2) for some q is an element of (1, 2). If alpha is an element of R 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, in the sense that the perturbation v(0) can be arbitrarily large, and our smallness assumption on the circulation alpha is independent of the domain Omega.Keywords
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