Comptes Rendus
Mathematical Problems in Mechanics
Very weak solutions for the stationary Oseen and Navier–Stokes equations
[Solutions très faibles pour les équations stationnaires d'Oseen et de Navier–Stokes]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 335-339.

Nous considérons les équations stationnaires d'Oseen et de Navier–Stokes dans un ouvert borné connexe et de classe C1,1 de R3. Nous donnons ici une nouvelle preuve plus simple de l'existence de solutions très faibles (u,q)Lp(Ω)×W1,p(Ω) correspondant à des données au bord dans W1/p,p(Γ). Ces solutions sont obtenues sans hypothèse de petitesse des forces extérieures. On obtient aussi des résultats de régularité dans des espaces de Sobolev fractionnaires.

We consider the stationary Oseen and Navier–Stokes equations in a bounded connected domain of class C1,1 of R3. Here we give a new and simpler proof of the existence of very weak solutions (u,q)Lp(Ω)×W1,p(Ω) corresponding to boundary data in W1/p,p(Γ). These solutions are obtained without imposing smallness assumptions on the exterior forces. We also obtain regularity results in fractional Sobolev spaces.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.12.021

Chérif Amrouche 1 ; María Ángeles Rodríguez-Bellido 2

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
2 Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Aptdo. de Correos 1160, 41080 Sevilla, Spain
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Chérif Amrouche; María Ángeles Rodríguez-Bellido. Very weak solutions for the stationary Oseen and Navier–Stokes equations. Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 335-339. doi : 10.1016/j.crma.2009.12.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.12.021/

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