Estimate of the pressure when its gradient is the divergence of a measure. Applications
In this paper, a W−1,N estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on RN , or on a regular bounded open set of RN . The proof is based partially on the Strauss inequality [Strauss, Partial Differential Equations: Proc. Symp. Pure Math. 23 (1973)...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/42083 |
| Acceso en línea: | http://hdl.handle.net/11441/42083 https://doi.org/10.1051/cocv/2010037 |
| Access Level: | acceso abierto |
| Palabra clave: | Pressure Navier-Stokes equation div-curl measure data fundamental solution |
| Sumario: | In this paper, a W−1,N estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on RN , or on a regular bounded open set of RN . The proof is based partially on the Strauss inequality [Strauss, Partial Differential Equations: Proc. Symp. Pure Math. 23 (1973) 207–214] in dimension two, and on a recent result of Bourgain and Brezis [J. Eur. Math. Soc. 9 (2007) 277–315] in higher dimension. The estimate is used to derive a representation result for divergence free distributions which read as the divergence of a measure, and to prove an existence result for the stationary Navier-Stokes equation when the viscosity tensor is only in L1. |
|---|