Article
Very weak solutions for the stationary Stokes equations
Author/s | Amrouche, Chérif
Rodríguez Bellido, María Ángeles |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2010-02 |
Deposit Date | 2016-04-22 |
Published in |
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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 ... 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. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España Junta de Andalucía |
Project ID. | MTM2006-07932
P06-FQM-02373 |
Citation | 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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