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Long-time asymptotics
for two-dimensional exterior flows with small circulation at
infinity
Thierry Gallay and Yasunori Maekawa |
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Vol. 6 (2013), No. 4, 973–991
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Abstract |
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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 . |
Keywords
Navier–Stokes equations, exterior domains, long-time
asymptotics, Oseen vortices
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Mathematical Subject Classification 2010
Primary: 35B35, 35Q30, 76D05, 76D17
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Milestones
Received: 28 February 2012
Accepted: 6 August 2012
Published: 21 August 2013
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Authors |
| Thierry Gallay | |
| Institut Fourier Université de Grenoble I 100 rue des Maths B.P. 74 38402 Saint-Martin-d’Hères France |
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| http://www-fourier.ujf-grenoble.fr/~gallay | |
| Yasunori Maekawa | |
| Department of Mathematics Graduate School of Science Kobe University 1-1 Rokkodai, Nada-ku Kobe 657-8501 Japan |
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| http://www.math.kobe-u.ac.jp/home-j/yasunori.html | |
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