Abstract
We consider the incompressible Navier–Stokes equations in a two-dimensional exterior domain , with no-slip boundary conditions. Our initial data are of the form , where is the Oseen vortex with unit circulation at infinity and is a solenoidal perturbation belonging to for some . If is sufficiently small, we show that the solution behaves asymptotically in time like the self-similar Oseen vortex with circulation . This is a global stability result, in the sense that the perturbation can be arbitrarily large, and our smallness assumption on the circulation is independent of the domain .
Citation
Thierry Gallay. Yasunori Maekawa. "Long-time asymptotics for two-dimensional exterior flows with small circulation at infinity." Anal. PDE 6 (4) 973 - 991, 2013. https://doi.org/10.2140/apde.2013.6.973
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