Titre :

Global weak solutions to the compressible quantum navier-stokes equation and its semi-classical limit

Auteur(s) :

Lacroix-Violet, Ingrid [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Vasseur, Alexis [Auteur]
University of Texas at Austin [Austin]

Titre de la revue :

Journal de Mathématiques Pures et Appliquées

Pagination :

191-210

Éditeur :

Elsevier

Date de publication :

2018

ISSN :

0021-7824

Discipline(s) HAL :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

Résumé en anglais : [en]

This paper is dedicated to the construction of global weak solutions to the quantum Navier-Stokes equation, for any initial value with bounded energy and entropy. The construction is uniform with respect to the Planck ...
Lire la suite >This paper is dedicated to the construction of global weak solutions to the quantum Navier-Stokes equation, for any initial value with bounded energy and entropy. The construction is uniform with respect to the Planck constant. This allows to perform the semi-classical limit to the associated compressible Navier-Stokes equation. One of the difficulty of the problem is to deal with the degenerate viscosity, together with the lack of integrability on the velocity. Our method is based on the construction of weak solutions that are renormalized in the velocity variable. The existence, and stability of these solutions do not need the Mellet-Vasseur inequality.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL