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Article Dans Une Revue Analysis & PDE Année : 2013

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

Thierry Gallay
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Résumé

We consider the incompressible Navier-Stokes equations in a two-dimensional exterior domain Ω, with no-slip boundary conditions. Our initial data are of the form u 0 = αΘ 0 + v 0 , where Θ 0 is the Oseen vortex with unit circulation at infinity and v 0 is a solenoidal perturbation belonging to L 2 (Ω) 2 ∩ L q (Ω) 2 for some q ∈ (1, 2). If α ∈ R is sufficiently small, we show that the solution behaves asymptotically in time like the self-similar Oseen vortex with circulation α. 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 α is independent of the domain Ω.
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Dates et versions

hal-01227482 , version 1 (11-11-2015)

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Thierry Gallay, Yasunori Maekawa. Long-time asymptotics for two-dimensional exterior flows with small circulation at infinity. Analysis & PDE, 2013, 6, 4 (973–991), ⟨10.2140/apde.2013.6.973⟩. ⟨hal-01227482⟩
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