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- W1636706315 abstract "The asymptotic behavior of the vorticity for the steady incompressible Navier–Stokes equations in a two-dimensional exterior domain is described in the case where the velocity at infinity u∞ is nonzero. It is well known that the asymptotic behavior of the velocity field is given by the fundamental solution of the Oseen system which is the linearization of the Navier–Stokes equation around u∞. Concerning the vorticity, the previous asymptotic expansions were relevant only inside a parabolic region called the wake region. Here we present an asymptotic expansion for the vorticity relevant everywhere. Surprisingly, the found asymptotic behavior is not given by the Oseen linearization and has a power of decay that depends on the data. This strange behavior is specific to the two-dimensional problem and is not present in three dimensions. Le comportement asymptotique de la vorticité pour les équations de Navier–Stokes incompressibles dans un domaine extérieur bidimensionnel est décrit dans le cas où la vitesse à l'infini u∞ est non nulle. Il est bien connu que le développement asymptotique du champ de vitesses est donné par la solution fondamentale de l'équation d'Oseen, qui correspond à la linéarisation des équations de Navier–Stokes autour de u∞. Concernant la vorticité, les développements asymptotiques antérieurs étaient pertinents seulement dans la région parabolique du sillage. Dans cet article, on présente un développement asymptotique pour la vorticité pertinent partout. De manière surprenante, le comportement asymptotique n'est pas donné par la linéarisation d'Oseen et possède une décroissance dépendant des données. Cette particularité est spécifique au problème bidimensionnel et n'est pas présente en trois dimensions." @default.
- W1636706315 created "2016-06-24" @default.
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- W1636706315 date "2017-10-01" @default.
- W1636706315 modified "2023-10-14" @default.
- W1636706315 title "Optimal asymptotic behavior of the vorticity of a viscous flow past a two-dimensional body" @default.
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- W1636706315 doi "https://doi.org/10.1016/j.matpur.2017.04.003" @default.
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