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)...

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Detalles Bibliográficos
Autores: Briane, Marc, Casado Díaz, Juan
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
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spelling Estimate of the pressure when its gradient is the divergence of a measure. ApplicationsBriane, MarcCasado Díaz, JuanPressureNavier-Stokes equationdiv-curlmeasure datafundamental solutionIn 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.Ministerio de Ciencia e InnovaciónEDP SciencesEcuaciones Diferenciales y Análisis NuméricoMinisterio de Ciencia e Innovación (MICIN). España2011info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/42083https://doi.org/10.1051/cocv/2010037reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésESAIM: Control, Optimisation and Calculus of Variations, 17 (4), 1066-1087.MTM2008-00306Parisinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/420832026-06-17T12:51:07Z
dc.title.none.fl_str_mv Estimate of the pressure when its gradient is the divergence of a measure. Applications
title Estimate of the pressure when its gradient is the divergence of a measure. Applications
spellingShingle Estimate of the pressure when its gradient is the divergence of a measure. Applications
Briane, Marc
Pressure
Navier-Stokes equation
div-curl
measure data
fundamental solution
title_short Estimate of the pressure when its gradient is the divergence of a measure. Applications
title_full Estimate of the pressure when its gradient is the divergence of a measure. Applications
title_fullStr Estimate of the pressure when its gradient is the divergence of a measure. Applications
title_full_unstemmed Estimate of the pressure when its gradient is the divergence of a measure. Applications
title_sort Estimate of the pressure when its gradient is the divergence of a measure. Applications
dc.creator.none.fl_str_mv Briane, Marc
Casado Díaz, Juan
author Briane, Marc
author_facet Briane, Marc
Casado Díaz, Juan
author_role author
author2 Casado Díaz, Juan
author2_role author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
Ministerio de Ciencia e Innovación (MICIN). España
dc.subject.none.fl_str_mv Pressure
Navier-Stokes equation
div-curl
measure data
fundamental solution
topic Pressure
Navier-Stokes equation
div-curl
measure data
fundamental solution
description 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.
publishDate 2011
dc.date.none.fl_str_mv 2011
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/42083
https://doi.org/10.1051/cocv/2010037
url http://hdl.handle.net/11441/42083
https://doi.org/10.1051/cocv/2010037
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv ESAIM: Control, Optimisation and Calculus of Variations, 17 (4), 1066-1087.
MTM2008-00306
Paris
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv EDP Sciences
publisher.none.fl_str_mv EDP Sciences
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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