On the very weak solution for the Oseen and Navier-Stokes equations

Chérif Amrouche; María Ángeles Rodríguez-Bellido

doi:10.3934/dcdss.2010.3.159

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2010, Volume 3, Issue 2: 159-183. Doi: 10.3934/dcdss.2010.3.159

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On the very weak solution for the Oseen and Navier-Stokes equations

Chérif Amrouche^1, and
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
2.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Aptdo. de Correos 1160 - 41080 Sevilla

Received: June 2009

Revised: October 2009

Published: June 2010

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Abstract

We study the existence of very weak solutions regularity for the Stokes, Oseen and Navier-Stokes system when non-smooth Dirichlet boundary data for the velocity are considered in domains of class $C^{1,1}$. In the Navier-Stokes case, the results will be valid for external forces non necessarily small. Regularity results for more regular data will be also discussed.

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Mathematics Subject Classification: Primary: 35Q30; Secondary: 76D03, 76D05, 76D07.

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