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June  2010, 3(2): 159-183. doi: 10.3934/dcdss.2010.3.159

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, Spain

Received  June 2009 Revised  October 2009 Published  April 2010

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.
Keywords: Stokes equations, Navier-Stokes equations, Stationary Solutions., Oseen equations, Very weak solutions.
Mathematics Subject Classification: Primary: 35Q30; Secondary: 76D03, 76D05, 76D0.
Citation: Chérif Amrouche, María Ángeles Rodríguez-Bellido. On the very weak solution for the Oseen and Navier-Stokes equations. Discrete & Continuous Dynamical Systems - S, 2010, 3 (2) : 159-183. doi: 10.3934/dcdss.2010.3.159
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