Article
Estimate of the pressure when its gradient is the divergence of a measure. Applications
Author/s | Briane, Marc
Casado Díaz, Juan |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2011 |
Deposit Date | 2016-06-09 |
Published in |
|
Abstract | 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 ... 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. |
Funding agencies | Ministerio de Ciencia e Innovación (MICIN). España |
Project ID. | MTM2008-00306 |
Citation | Briane, M. y Casado Díaz, J. (2011). Estimate of the pressure when its gradient is the divergence of a measure. Applications. ESAIM: Control, Optimisation and Calculus of Variations, 17 (4), 1066-1087. |
Files | Size | Format | View | Description |
---|---|---|---|---|
Estimate of the pressure when ... | 343.9Kb | [PDF] | View/ | |