Some controllability results for the N-Dimensional Navier-Stokes and Boussinesq systems with N-1 scalar controls

In this paper we deal with some controllability problems for systems of the Navier-Stokes and Boussinesq kind with distributed controls supported in small sets. Our main aim is to control N-dimensional systems (N + 1 scalar unknowns in the case of the Navier–Stokes equations) with N − 1 scalar contr...

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Autores: Fernández Cara, Enrique, Guerrero Rodríguez, Sergio, Imanuvilov, Oleg Yu, Puel, Jean-Pierre
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2006
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/41449
Acceso en línea:http://hdl.handle.net/11441/41449
https://doi.org/10.1137/04061965X
Access Level:acceso abierto
Palabra clave:Navier–Stokes system
exact controllability
Carleman inequalities
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spelling Some controllability results for the N-Dimensional Navier-Stokes and Boussinesq systems with N-1 scalar controlsFernández Cara, EnriqueGuerrero Rodríguez, SergioImanuvilov, Oleg YuPuel, Jean-PierreNavier–Stokes systemexact controllabilityCarleman inequalitiesIn this paper we deal with some controllability problems for systems of the Navier-Stokes and Boussinesq kind with distributed controls supported in small sets. Our main aim is to control N-dimensional systems (N + 1 scalar unknowns in the case of the Navier–Stokes equations) with N − 1 scalar control functions. In a first step, we present some global Carleman estimates for suitable adjoint problems of linearized Navier–Stokes and Boussinesq systems. In this way, we obtain null controllability properties for these systems. Then, we deduce results concerning the local exact controllability to the trajectories. We also present (global) null controllability results for some (truncated) approximations of the Navier–Stokes equations.Ministerio de Educación y CienciaSociety for Industrial and Applied MathematicsEcuaciones Diferenciales y Análisis NuméricoMinisterio de Educación y Ciencia (MEC). España2006info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/41449https://doi.org/10.1137/04061965Xreponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésSIAM Journal on Control and Optimization, 45 (1), 146-173.BFM2003–06446info:eu-repo/semantics/openAccessoai:idus.us.es:11441/414492026-06-17T12:51:07Z
dc.title.none.fl_str_mv Some controllability results for the N-Dimensional Navier-Stokes and Boussinesq systems with N-1 scalar controls
title Some controllability results for the N-Dimensional Navier-Stokes and Boussinesq systems with N-1 scalar controls
spellingShingle Some controllability results for the N-Dimensional Navier-Stokes and Boussinesq systems with N-1 scalar controls
Fernández Cara, Enrique
Navier–Stokes system
exact controllability
Carleman inequalities
title_short Some controllability results for the N-Dimensional Navier-Stokes and Boussinesq systems with N-1 scalar controls
title_full Some controllability results for the N-Dimensional Navier-Stokes and Boussinesq systems with N-1 scalar controls
title_fullStr Some controllability results for the N-Dimensional Navier-Stokes and Boussinesq systems with N-1 scalar controls
title_full_unstemmed Some controllability results for the N-Dimensional Navier-Stokes and Boussinesq systems with N-1 scalar controls
title_sort Some controllability results for the N-Dimensional Navier-Stokes and Boussinesq systems with N-1 scalar controls
dc.creator.none.fl_str_mv Fernández Cara, Enrique
Guerrero Rodríguez, Sergio
Imanuvilov, Oleg Yu
Puel, Jean-Pierre
author Fernández Cara, Enrique
author_facet Fernández Cara, Enrique
Guerrero Rodríguez, Sergio
Imanuvilov, Oleg Yu
Puel, Jean-Pierre
author_role author
author2 Guerrero Rodríguez, Sergio
Imanuvilov, Oleg Yu
Puel, Jean-Pierre
author2_role author
author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
Ministerio de Educación y Ciencia (MEC). España
dc.subject.none.fl_str_mv Navier–Stokes system
exact controllability
Carleman inequalities
topic Navier–Stokes system
exact controllability
Carleman inequalities
description In this paper we deal with some controllability problems for systems of the Navier-Stokes and Boussinesq kind with distributed controls supported in small sets. Our main aim is to control N-dimensional systems (N + 1 scalar unknowns in the case of the Navier–Stokes equations) with N − 1 scalar control functions. In a first step, we present some global Carleman estimates for suitable adjoint problems of linearized Navier–Stokes and Boussinesq systems. In this way, we obtain null controllability properties for these systems. Then, we deduce results concerning the local exact controllability to the trajectories. We also present (global) null controllability results for some (truncated) approximations of the Navier–Stokes equations.
publishDate 2006
dc.date.none.fl_str_mv 2006
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/11441/41449
https://doi.org/10.1137/04061965X
url http://hdl.handle.net/11441/41449
https://doi.org/10.1137/04061965X
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv SIAM Journal on Control and Optimization, 45 (1), 146-173.
BFM2003–06446
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 Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
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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