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Regularity of the global attractor and finite-dimensional behavior for the second grade fluid equations

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPAICU, Marius
hal.structure.identifierUniversité Paris-Sud - Paris 11 [UP11]
dc.contributor.authorREKALO, Andrey
hal.structure.identifierLaboratoire de Mathématiques d'Orsay [LMO]
dc.contributor.authorRAUGEL, Geneviève
dc.date.accessioned2024-04-04T02:17:24Z
dc.date.available2024-04-04T02:17:24Z
dc.date.issued2012
dc.identifier.issn0022-0396
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189225
dc.description.abstractEnThis paper is devoted to the large time behavior and especially to the regularity of the global attractor of the second grade fluid equations in the two-dimensional torus. We first recall that, for any size of the material coefficient alpha > 0, these equations are globally well posed and admit a compact global attractor A(alpha) in (H-3(T-2))(2). We prove that, for any alpha > 0, there exists beta(alpha) > 0, such that A(alpha) belongs to (H3+beta(alpha) (T-2))(2) if the forcing term is in (H1+beta(alpha) (T-2))(2). We also show that this attractor is contained in any Sobolev space (H3+m(T-2))(2) provided that alpha is small enough and the forcing term is regular enough. These arguments lead also to a new proof of the existence of the compact global attractor A(alpha). Furthermore we prove that on A(alpha), the second grade fluid system can be reduced to a finite-dimensional system of ordinary differential equations with an infinite delay. Moreover, the existence of a finite number of determining modes for the equations of the second grade fluid is established.
dc.language.isoen
dc.publisherElsevier
dc.title.enRegularity of the global attractor and finite-dimensional behavior for the second grade fluid equations
dc.typeArticle de revue
dc.identifier.doi10.1016/j.jde.2011.10.015
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.journalJournal of Differential Equations
bordeaux.page3695-3751
bordeaux.volume252
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue6
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00994720
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00994720v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Differential%20Equations&rft.date=2012&rft.volume=252&rft.issue=6&rft.spage=3695-3751&rft.epage=3695-3751&rft.eissn=0022-0396&rft.issn=0022-0396&rft.au=PAICU,%20Marius&REKALO,%20Andrey&RAUGEL,%20Genevi%C3%A8ve&rft.genre=article


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