ARNAUDON, Marc; CRUZEIRO, Ana Bela; LÉONARD, Christian; ZAMBRINI, Jean-Claude

Métadonnées

Licence d’utilisation du document

ARNAUDON, Marc
Institut de Mathématiques de Bordeaux [IMB]

CRUZEIRO, Ana Bela
Grupo de Fisica Matematica [GFMUL]

LÉONARD, Christian
Modélisation aléatoire de Paris X [MODAL'X]
Fédération Parisienne de Modélisation Mathématique [FP2M]

Langue

Article de revue

Ce document a été publié dans

Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques. 2020, vol. 56, n° 3, p. 2211-2235

Institut Henri Poincaré (IHP)

Résumé en anglais

In 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.< Réduire

Mots clés en anglais

Incompressible viscid fluids

entropy minimization

diffusion processes

convex duality

stochastic velocities

Navier-Stokes equation

URI

https://oskar-bordeaux.fr/handle/20.500.12278/193698

Project ANR

Modèles Mathématiques et Economiques de la Dynamique, de l'Incertitude et des Interactions - ANR-11-LABX-0023

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251