Existence of solution for a density-dependent magnetohydrodynamic equation

Jean-Frédéric Gerbeau (1) , Claude Le Bris (1, 2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MICMAC - Methods and engineering of multiscale computing from atom to continuum

We prove a global-in-time existence result of a weak solution for a magnetohydrodynamic (MHD) problem set in a bounded domain of R^3. The fluid is supposed to be incompressible but with an unhomogeneous density, viscosity and electrical conductivity. The displacement currents are neglected in the time dependent Maxwell equations. The model describes in particular the flow of two immiscible fluids in presence of a magnetic field.

Mots clés: MHD; existence theorem; multi-fluid flows

Domaines: Analyse numérique [math.NA]

Jean-Frédéric Gerbeau, Claude Le Bris. Existence of solution for a density-dependent magnetohydrodynamic equation. Advances in Differential Equations, 1997, 2 (3), pp.427-452. ⟨hal-00690237⟩