Incompressible flows with piecewise constant density - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2013

Incompressible flows with piecewise constant density

Résumé

We investigate the incompressible Navier-Stokes equations with variable density. The aim is to prove existence and uniqueness results in the case of discontinuous ini- tial density. In dimension n = 2, 3, assuming only that the initial density is bounded and bounded away from zero, and that the initial velocity is smooth enough, we get the local-in-time existence of unique solutions. Uniqueness holds in any dimension and for a wider class of velocity fields. Let us emphasize that all those results are true for piecewise constant densities with arbitrarily large jumps. Global results are established in dimension two if the density is close enough to a positive constant, and in n-dimension if, in addition, the initial velocity is small. The Lagrangian formula- tion for describing the flow plays a key role in the analysis that is proposed in the present paper.
Fichier principal
Vignette du fichier
dis-01-02.pdf (281.41 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00676603 , version 1 (05-03-2012)

Identifiants

Citer

Raphaël Danchin, Piotr Bogusław Mucha. Incompressible flows with piecewise constant density. Archive for Rational Mechanics and Analysis, 2013, 207, pp.991-1023. ⟨10.1007/s00205-012-0586-4⟩. ⟨hal-00676603⟩
155 Consultations
232 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More