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Séminaire du LJLL - 16 06 2017 14h00 : Y. Maekawa
Yasunori Maekawa (Université de Kyoto)
On the stability of the physically reasonable solution to the two-dimensional Navier-Stokes equations
Résumé
The flow past an obstacle is a fundamental object in fluid mechanics. In 1967 R. Finn and D.R. Smith proved the existence and uniqueness of a stationary solution that they called "the physically reasonable solution" to the Navier-Stokes equations in a two-dimensional exterior domain modeling this type of flows, when the Reynolds number is sufficiently small. The asymptotic behavior of this solution at infinity in space has been studied in details and is well understood by now, while its stability remained an open problem due to difficulties specific to the two-dimensionality.
In this talk we show that the physically reasonable solution constructed by Finn and Smith is asymptotically stable with respect to small and well-localized initial perturbations.