Mathematical Problems in Mechanics/Partial Differential Equations
On the existence of solutions in weighted Sobolev spaces for the exterior Oseen problem
Comptes Rendus. Mathématique, Volume 341 (2005) no. 9, pp. 587-592.

In this Note, we present existence and uniqueness results for the exterior Oseen problem. In order to control the behavior at infinity of functions, we use as functional framework weighted Sobolev spaces. The results rely on a Lp-theory for 1<p<.

Dans cette Note, on présente des résultats d'existence et d'unicité pour les équations d'Oseen posées dans des domaines extérieurs de R3. Le comportement à l'infini des solutions est décrit par l'utilisation des espaces de Sobolev avec poids. L'étude repose sur une théorie Lp, avec 1<p<.

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DOI: 10.1016/j.crma.2005.09.007
Amrouche, Chérif 1; Razafison, Ulrich 1

1 Laboratoire de mathématiques appliquées, CNRS UMR 5142, université de Pau et des pays de l'Adour, IPRA, avenue de l'Université, 64000 Pau, France
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Amrouche, Chérif; Razafison, Ulrich. On the existence of solutions in weighted Sobolev spaces for the exterior Oseen problem. Comptes Rendus. Mathématique, Volume 341 (2005) no. 9, pp. 587-592. doi : 10.1016/j.crma.2005.09.007. http://www.numdam.org/articles/10.1016/j.crma.2005.09.007/

[1] C. Amrouche, U. Razafison, The stationary Oseen equations in R3. An approach in weighted Sobolev spaces, Preprint no 2004/09, Université de Pau et des Pays de l'Adour (2004); J. Math. Fluid Mech., submitted for publication

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