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

Thierry Gallay; Yasunori Maekawa

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arXiv · 1202.4969

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

Thierry Gallay·Yasunori Maekawa

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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.

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Thierry Gallay, Yasunori Maekawa. 2012-02-22. Long-time asymptotics for two-dimensional exterior flows with small circulation at infinity. https://arxiv.org/abs/1202.4969

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