Uniform local null control of the Leray-α model

This paper deals with the distributed and boundary controllability of the so called Leray-α model. This is a regularized variant of the Navier−Stokes system (α is a small positive parameter) that can also be viewed as a model for turbulent flows. We prove that the Leray-α equations are locally null...

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Detalles Bibliográficos
Autores: Dias Araruna, Fágner, Fernández Cara, Enrique, Araujo de Souza, Diego
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2014
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/41441
Acceso en línea:http://hdl.handle.net/11441/41441
https://doi.org/10.1051/cocv/2014011
Access Level:acceso abierto
Palabra clave:Null controllability
Carleman inequalities
Leray-α model
Navier−Stokes equations
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spelling Uniform local null control of the Leray-α modelDias Araruna, FágnerFernández Cara, EnriqueAraujo de Souza, DiegoNull controllabilityCarleman inequalitiesLeray-α modelNavier−Stokes equationsThis paper deals with the distributed and boundary controllability of the so called Leray-α model. This is a regularized variant of the Navier−Stokes system (α is a small positive parameter) that can also be viewed as a model for turbulent flows. We prove that the Leray-α equations are locally null controllable, with controls bounded independently of α. We also prove that, if the initial data are sufficiently small, the controls converge as α → 0+ to a null control of the Navier−Stokes equations. We also discuss some other related questions, such as global null controllability, local and global exact controllability to the trajectories, etc.Instituto Nacional de Ciência e Tecnologia de MatemáticaCoordenação de aperfeiçoamento de pessoal de nivel superiorConselho Nacional de Desenvolvimento Científico e TecnológicoMinisterio de Educación y Ciencia (España) MTM2006-07932 MTM2010-15592EDP SciencesEcuaciones Diferenciales y Análisis Numérico2014info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/41441https://doi.org/10.1051/cocv/2014011reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésESAIM: Control, Optimisation and Calculus of Variations, 20 (4), 1181-1202.info:eu-repo/grantAgreement/MINECO/MTM2006-07932/info:eu-repo/grantAgreement/MINECO/MTM2010-15592/http://dx.doi.org/10.1051/cocv/2014011info:eu-repo/semantics/openAccessoai:idus.us.es:11441/414412026-06-17T12:51:07Z
dc.title.none.fl_str_mv Uniform local null control of the Leray-α model
title Uniform local null control of the Leray-α model
spellingShingle Uniform local null control of the Leray-α model
Dias Araruna, Fágner
Null controllability
Carleman inequalities
Leray-α model
Navier−Stokes equations
title_short Uniform local null control of the Leray-α model
title_full Uniform local null control of the Leray-α model
title_fullStr Uniform local null control of the Leray-α model
title_full_unstemmed Uniform local null control of the Leray-α model
title_sort Uniform local null control of the Leray-α model
dc.creator.none.fl_str_mv Dias Araruna, Fágner
Fernández Cara, Enrique
Araujo de Souza, Diego
author Dias Araruna, Fágner
author_facet Dias Araruna, Fágner
Fernández Cara, Enrique
Araujo de Souza, Diego
author_role author
author2 Fernández Cara, Enrique
Araujo de Souza, Diego
author2_role author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
dc.subject.none.fl_str_mv Null controllability
Carleman inequalities
Leray-α model
Navier−Stokes equations
topic Null controllability
Carleman inequalities
Leray-α model
Navier−Stokes equations
description This paper deals with the distributed and boundary controllability of the so called Leray-α model. This is a regularized variant of the Navier−Stokes system (α is a small positive parameter) that can also be viewed as a model for turbulent flows. We prove that the Leray-α equations are locally null controllable, with controls bounded independently of α. We also prove that, if the initial data are sufficiently small, the controls converge as α → 0+ to a null control of the Navier−Stokes equations. We also discuss some other related questions, such as global null controllability, local and global exact controllability to the trajectories, etc.
publishDate 2014
dc.date.none.fl_str_mv 2014
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/11441/41441
https://doi.org/10.1051/cocv/2014011
url http://hdl.handle.net/11441/41441
https://doi.org/10.1051/cocv/2014011
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, 20 (4), 1181-1202.
info:eu-repo/grantAgreement/MINECO/MTM2006-07932/
info:eu-repo/grantAgreement/MINECO/MTM2010-15592/
http://dx.doi.org/10.1051/cocv/2014011
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 15,300724

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