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Very weak solutions for the stationary Stokes equations

Opened Access Very weak solutions for the stationary Stokes equations

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Autor: Amrouche, Chérif
Rodríguez Bellido, María Ángeles
Departamento: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Fecha: 2010-02
Publicado en: Comptes rendus mathématique, 348 (3-4), 223-228
Tipo de documento: Artículo
Resumen: 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.
Cita: Amrouche, C. y Rodríguez Bellido, M.Á. (2010). Very weak solutions for the stationary Stokes equations. Comptes rendus mathématique, 348 (3-4), 223-228.
Tamaño: 302.0Kb
Formato: PDF

URI: http://hdl.handle.net/11441/40278

DOI: http://dx.doi.org/10.1016/j.crma.2009.12.020

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