Résultats d’existence dans des espaces critiques pour le système de la MHD inhomogène
Annales mathématiques Blaise Pascal, Tome 14 (2007) no. 1, pp. 103-148.

Nous démontrons dans cet article que le système MHD tridimensionnel à densité et viscosité variables est localement bien posé lorsque (ρ0-1-1,u0,B0)B˙p13p(3)×B˙p13p-1(3)×B˙p13p-1(3), pour p]1,3] et la densité initiale est proche d’une constante strictement positive. Nous démontrons également un résultat d’existence et d’unicité dans l’espace de Sobolev H32+α(3)×H32-1+α(3)×H32-1+α(3) pour α>0, sans aucune condition de petitesse sur la densité.

In this article, we show that the 3D MHD system with variable density and viscosity is locally well-posed in the Besov space B˙p13p(3)×B˙p13p-1(3) for 1<p3 and that the initial density approaches a positive constant. Moreover, we prove existence and uniqueness in the Sobolev space H32+α(3)×H32-1+α(3) for α>0, without smallness condition for the density.

DOI : 10.5802/ambp.230
Classification : 35Q30, 35B30, 76D03, 76D05
Mots-clés : Existence, uniqueness, nonhomogeneous model of magnetohydrodynamics

Abidi, Hammadi 1 ; Hmidi, Taoufik 2

1 IRMAR, Université de Rennes 1 Campus de Beaulieu 35042 Rennes cedex FRANCE
2 Institut de Recherches Mathématiques de Rennes Université de Rennes 1 Campus de Beaulieu 263, avenue du Général Leclerc CS 74205 35042 Rennes Cedex FRANCE
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Abidi, Hammadi; Hmidi, Taoufik. Résultats d’existence dans des espaces critiques pour le système de la MHD inhomogène. Annales mathématiques Blaise Pascal, Tome 14 (2007) no. 1, pp. 103-148. doi : 10.5802/ambp.230. https://www.numdam.org/articles/10.5802/ambp.230/

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