Global weak solutions for quantum isothermal fluids - Département de mathématiques Accéder directement au contenu
Article Dans Une Revue Annales de l'Institut Fourier Année : 2022

Global weak solutions for quantum isothermal fluids

Résumé

We construct global weak solutions to isothermal quantum Navier-Stokes equations, with or without Korteweg term, in the whole space of dimension at most three. Instead of working on the initial set of unknown functions, we consider an equivalent reformulation, based on a time-dependent rescaling, that we introduced in a previous paper to study the large time behavior, and which provides suitable a priori estimates, as opposed to the initial formulation where the potential energy is not signed. We proceed by working on tori whose size eventually becomes infinite. On each fixed torus, we consider the equations in the presence of drag force terms. Such equations are solved by regularization, and the limit where the drag force terms vanish is treated by resuming the notion of renormalized solution developed by I. Lacroix-Violet and A. Vasseur. We also establish global existence of weak solutions for the isothermal Korteweg equation (no viscosity), when initial data are well-prepared, in the sense that they stem from a Madelung transform.
Fichier principal
Vignette du fichier
existence.pdf (481.76 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02116596 , version 1 (01-05-2019)
hal-02116596 , version 2 (03-03-2021)

Identifiants

Citer

Rémi Carles, Kleber Carrapatoso, Matthieu Hillairet. Global weak solutions for quantum isothermal fluids. Annales de l'Institut Fourier, 2022, 72 (6), pp.2241-2298. ⟨10.5802/aif.3489⟩. ⟨hal-02116596v2⟩
344 Consultations
128 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More