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Generalized stochastic flows and applications to incompressible viscous fluids

hal.structure.identifierDep. Nonlinear Analysis Institute of Mathematics NAS Ukraine
dc.contributor.authorANTONIOUK, Alexandra
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorARNAUDON, Marc
hal.structure.identifiergrupo de fisica matematica
dc.contributor.authorCRUZEIRO, Ana Bela
dc.date.accessioned2024-04-04T03:20:56Z
dc.date.available2024-04-04T03:20:56Z
dc.date.created2013-11-01
dc.date.issued2014-06-02
dc.identifier.issn0007-4497
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194625
dc.description.abstractEnWe introduce a notion of generalized stochastic flows on manifolds, that extends to the viscous case the one defined by Brenier for perfect fluids. Their kinetic energy extends the classical kinetic energy to Brownian flows, defined as the $L^2$ norm of their drift. We prove that there exists a generalized flow which realizes the infimum of the kinetic energy among all generalized flows with prescribed initial and final configuration. We also construct generalized flows with prescribed drift and kinetic energy smaller than the $L^2$ norm of the drift. The results are actually presented for general $L^q$ norms, thus including not only the Navier-Stokes equations but also other equations such as the porous media.
dc.description.sponsorship/ - ANR-09-BLAN-0364
dc.language.isoen
dc.publisherElsevier
dc.title.enGeneralized stochastic flows and applications to incompressible viscous fluids
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Probabilités [math.PR]
bordeaux.journalBulletin des Sciences Mathématiques
bordeaux.page565-584
bordeaux.volume138
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue4
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01057528
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01057528v1
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