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An entropic interpolation problem for incompressible viscid fluids

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorARNAUDON, Marc
hal.structure.identifiergrupo de fisica matematica
dc.contributor.authorCRUZEIRO, Ana Bela
hal.structure.identifierModélisation aléatoire de Paris X [MODAL'X]
dc.contributor.authorLÉONARD, Christian
hal.structure.identifierGrupo de Fisica Matematica [GFMUL]
dc.contributor.authorZAMBRINI, Jean-Claude
dc.date2020
dc.date.accessioned2024-04-04T02:56:21Z
dc.date.available2024-04-04T02:56:21Z
dc.date.issued2020
dc.identifier.issn0246-0203
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192456
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 viscous 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 form 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 relation with viscous fluid dynamics is discussed.
dc.language.isoen
dc.publisherInstitut Henri Poincaré (IHP)
dc.title.enAn entropic interpolation problem for incompressible viscid fluids
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Probabilités [math.PR]
bordeaux.journalAnnales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02488041
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02488041v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Annales%20de%20l'Institut%20Henri%20Poincar%C3%A9%20(B)%20Probabilit%C3%A9s%20et%20Statistiques&rft.date=2020&rft.eissn=0246-0203&rft.issn=0246-0203&rft.au=ARNAUDON,%20Marc&CRUZEIRO,%20Ana%20Bela&L%C3%89ONARD,%20Christian&ZAMBRINI,%20Jean-Claude&rft.genre=article


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