A priori estimates for 3D incompressible current-vortex sheets

Coulombel, Jean-François; Morando, Alessandro; Secchi, Paolo; Trebeschi, Paola

Type de document :

Article dans une revue scientifique: Article original

DOI :

10.1007/s00220-011-1340-8

Titre :

A priori estimates for 3D incompressible current-vortex sheets

Auteur(s) :

Coulombel, Jean-François [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Morando, Alessandro [Auteur]
Dipartimento di Matematica [Universita di Brescia]
Secchi, Paolo [Auteur]
Dipartimento di Matematica [Universita di Brescia]
Trebeschi, Paola [Auteur]
Dipartimento di Matematica [Universita di Brescia]

Titre de la revue :

Communications in Mathematical Physics

Pagination :

247-275

Éditeur :

Springer Verlag

Date de publication :

2012-12-31

ISSN :

0010-3616

Mot(s)-clé(s) en anglais :

Magneto-hydrodynamics
incompressible fluids
current-vortex sheets
free boundary
stability

Discipline(s) HAL :

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

Résumé en anglais : [en]

We consider the free boundary problem for current-vortex sheets in ideal incompressible magneto-hydrodynamics. It is known that current-vortex sheets may be at most weakly (neutrally) stable due to the existence of surface ...
Lire la suite >We consider the free boundary problem for current-vortex sheets in ideal incompressible magneto-hydrodynamics. It is known that current-vortex sheets may be at most weakly (neutrally) stable due to the existence of surface waves solutions to the linearized equations. The existence of such waves may yield a loss of derivatives in the energy estimate of the solution with respect to the source terms. However, under a suitable stability condition satisfied at each point of the initial discontinuity and a flatness condition on the initial front, we prove an a priori estimate in Sobolev spaces for smooth solutions with no loss of derivatives. The result of this paper gives some hope for proving the local existence of smooth current-vortex sheets without resorting to a Nash-Moser iteration. Such result would be a rigorous confirmation of the stabilizing effect of the magnetic field on Kelvin-Helmholtz instabilities, which is well known in astrophysics.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Interaction d'ondes compressibles

Collections :