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Very weak solutions for the stationary Stokes equations


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Opened Access Very weak solutions for the stationary Stokes equations

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Author: Amrouche, Chérif
Rodríguez Bellido, María Ángeles
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2010-02
Published in: Comptes rendus mathématique, 348 (3-4), 223-228
Document type: Article
Abstract: The concept of very weak solution introduced by Giga [9] for the stationary Stokes equations has been intensively studied in the last years for the stationary Navier-Stokes equations. We give here a new and simpler proof of the existence of very weak solution for the stationary Navier-Stokes equations, based on density arguments and an adequate functional framework in order to define more rigourously the traces of non regular vector fields. We also obtain regularity results in fractional Sobolev spaces. All these results are obtained in the case of a bounded open set, connected of class C1,1 of R3 and can be extended to the Laplace’s equation and to other dimensions.
Cite: Amrouche, C. y Rodríguez Bellido, M.Á. (2010). Very weak solutions for the stationary Stokes equations. Comptes rendus mathématique, 348 (3-4), 223-228.
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DOI: 10.1016/j.crma.2009.12.020

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