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Local null controllability of the penalized Boussinesq system with a reduced number of controls

hal.structure.identifierUniversidad Autónoma de Madrid [UAM]
hal.structure.identifierFundación Deusto
dc.contributor.authorBÁRCENA-PETISCO, Jon Asier
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierControl And GEometry [CaGE]
hal.structure.identifierLaboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
dc.contributor.authorBALC'H, Kévin Le
dc.date.accessioned2024-04-04T02:46:26Z
dc.date.available2024-04-04T02:46:26Z
dc.date.issued2022
dc.identifier.issn2156-8472
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191551
dc.description.abstractEnIn this paper we consider the Boussinesq system with homogeneous Dirichlet boundary conditions and defined in a regular domain Ω ⊂ R^N for N = 2 and N = 3. The incompressibility condition of the fluid is replaced by its approximation by penalization with a small parameter ε > 0. We prove that our system is locally null controllable using a control with a restricted number of components, defined in an open set ω contained in Ω and whose cost is bounded uniformly when ε → 0. The proof is based on a linearization argument and the null-controllability of the linearized system is obtained by proving a new Carleman estimate for the adjoint system. This observability inequality is obtained thanks to the coercivity of some second order differential operator involving crossed derivatives.
dc.description.sponsorshipInitiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003
dc.language.isoen
dc.publisherAIMS
dc.subject.enCarleman inequality
dc.subject.enControllability
dc.subject.enNonlinear system
dc.subject.enPenalized Stokes system
dc.title.enLocal null controllability of the penalized Boussinesq system with a reduced number of controls
dc.typeArticle de revue
dc.identifier.doi10.3934/mcrf.2021038
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.description.sponsorshipEuropeDynamic Control and Numerics of Partial Differential Equations
bordeaux.journalMathematical Control and Related Fields
bordeaux.page641
bordeaux.volume12
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue3
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02913358
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02913358v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematical%20Control%20and%20Related%20Fields&rft.date=2022&rft.volume=12&rft.issue=3&rft.spage=641&rft.epage=641&rft.eissn=2156-8472&rft.issn=2156-8472&rft.au=B%C3%81RCENA-PETISCO,%20Jon%20Asier&BALC'H,%20K%C3%A9vin%20Le&rft.genre=article


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