Generalized stochastic Lagrangian paths for the Navier-Stokes equation
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ARNAUDON, Marc | |
| dc.contributor.author | CRUZEIRO, Ana Bela | |
| hal.structure.identifier | Institut de Mathématiques de Bourgogne [Dijon] [IMB] | |
| dc.contributor.author | FANG, Shizan | |
| dc.date.accessioned | 2024-04-04T03:15:18Z | |
| dc.date.available | 2024-04-04T03:15:18Z | |
| dc.date.issued | 2018 | |
| dc.identifier.issn | 0391-173X | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194139 | |
| dc.description.abstractEn | In 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.iso | en | |
| dc.publisher | Scuola Normale Superiore | |
| dc.title.en | Generalized stochastic Lagrangian paths for the Navier-Stokes equation | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.2422/2036-2145.201602_006 | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.identifier.arxiv | 1509.03491 | |
| bordeaux.journal | Annali della Scuola Normale Superiore di Pisa, Classe di Scienze | |
| bordeaux.page | 1033-1060 | |
| bordeaux.volume | 18 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01197123 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01197123v1 | |
| bordeaux.COinS | ctx_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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