An entropic interpolation problem for incompressible viscid fluids
LÉONARD, Christian
Modélisation aléatoire de Paris X [MODAL'X]
Fédération Parisienne de Modélisation Mathématique [FP2M]
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Modélisation aléatoire de Paris X [MODAL'X]
Fédération Parisienne de Modélisation Mathématique [FP2M]
LÉONARD, Christian
Modélisation aléatoire de Paris X [MODAL'X]
Fédération Parisienne de Modélisation Mathématique [FP2M]
< Leer menos
Modélisation aléatoire de Paris X [MODAL'X]
Fédération Parisienne de Modélisation Mathématique [FP2M]
Idioma
en
Article de revue
Este ítem está publicado en
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques. 2020, vol. 56, n° 3, p. 2211-2235
Institut Henri Poincaré (IHP)
Resumen en inglés
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 ...Leer más >
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.< Leer menos
Palabras clave en inglés
Incompressible viscid fluids
entropy minimization
diffusion processes
convex duality
stochastic velocities
Navier-Stokes equation
Proyecto ANR
Modèles Mathématiques et Economiques de la Dynamique, de l'Incertitude et des Interactions - ANR-11-LABX-0023
Orígen
Importado de HalCentros de investigación