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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorARNAUDON, Marc
hal.structure.identifierGrupo de Fisica Matematica [GFMUL]
dc.contributor.authorCRUZEIRO, Ana Bela
hal.structure.identifierModélisation aléatoire de Paris X [MODAL'X]
hal.structure.identifierFédération Parisienne de Modélisation Mathématique [FP2M]
dc.contributor.authorLÉONARD, Christian
hal.structure.identifierGrupo de Fisica Matematica [GFMUL]
dc.contributor.authorZAMBRINI, Jean-Claude
dc.date.accessioned2024-04-04T03:10:36Z
dc.date.available2024-04-04T03:10:36Z
dc.date.issued2020
dc.identifier.issn0246-0203
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193698
dc.description.abstractEnIn view of studying incompressible inviscid fluids, Brenier introduced in the late 80's a relaxation of a geodesic problem addressed by Arnold in 1966. Instead of inviscid fluids, the present paper is devoted to incompressible viscid fluids. A natural analogue of Brenier's problem is introduced, where generalized flows are no more supported by absolutely continuous paths, but by Brownian sample paths. It turns out that this new variational problem is an entropy minimization problem with marginal constraints entering the class of convex minimization problems. This paper explores the connection between this variational problem and Brenier's original problem. Its dual problem is derived and the general shape of its solution is described. Under the restrictive assumption that the pressure is a nice function, the kinematics of its solution is made explicit and its connection with the Navier-Stokes equation is established.
dc.description.sponsorshipModèles Mathématiques et Economiques de la Dynamique, de l'Incertitude et des Interactions - ANR-11-LABX-0023
dc.language.isoen
dc.publisherInstitut Henri Poincaré (IHP)
dc.subject.enIncompressible viscid fluids
dc.subject.enentropy minimization
dc.subject.endiffusion processes
dc.subject.enconvex duality
dc.subject.enstochastic velocities
dc.subject.enNavier-Stokes equation
dc.title.enAn entropic interpolation problem for incompressible viscid fluids
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.identifier.arxiv1704.02126
bordeaux.journalAnnales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
bordeaux.page2211-2235
bordeaux.volume56
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-01502673
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01502673v1
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