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Generalized stochastic Lagrangian paths for the Navier-Stokes equation

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorARNAUDON, Marc
dc.contributor.authorCRUZEIRO, Ana Bela
hal.structure.identifierInstitut de Mathématiques de Bourgogne [Dijon] [IMB]
dc.contributor.authorFANG, Shizan
dc.date.accessioned2024-04-04T03:15:18Z
dc.date.available2024-04-04T03:15:18Z
dc.date.issued2018
dc.identifier.issn0391-173X
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194139
dc.description.abstractEnIn the note added in proof of the seminal paper [Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math. 92 (1970), 102-163], Ebin and Marsden introduced the so-called correct Laplacian for the Navier-Stokes equation on a compact Riemannian manifold. In the spirit of Brenier's generalized flows for the Euler equation, we introduce a class of semimartingales on a compact Riemannian manifold. We prove that these semimartingales are critical points to the corresponding kinetic energy if and only if its drift term solves weakly the Navier-Stokes equation defined with Ebin-Marsden's Laplacian. We also show that for the torus case, classical solutions of the Navier-Stokes equation realize the minimum of the kinetic energy in a suitable class.
dc.language.isoen
dc.publisherScuola Normale Superiore
dc.title.enGeneralized stochastic Lagrangian paths for the Navier-Stokes equation
dc.typeArticle de revue
dc.identifier.doi10.2422/2036-2145.201602_006
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.identifier.arxiv1509.03491
bordeaux.journalAnnali della Scuola Normale Superiore di Pisa, Classe di Scienze
bordeaux.page1033-1060
bordeaux.volume18
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-01197123
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01197123v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Annali%20della%20Scuola%20Normale%20Superiore%20di%20Pisa,%20Classe%20di%20Scienze&rft.date=2018&rft.volume=18&rft.issue=3&rft.spage=1033-1060&rft.epage=1033-1060&rft.eissn=0391-173X&rft.issn=0391-173X&rft.au=ARNAUDON,%20Marc&CRUZEIRO,%20Ana%20Bela&FANG,%20Shizan&rft.genre=article


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