Advances in Differential Equations

Existence of solution for a density-dependent magnetohydrodynamic equation

J.-F. Gerbeau and C. Le Bris

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We prove a global-in-time existence result of a weak solution for a magnetohydrodynamic (MHD) problem set in a bounded domain of $\mathbb{R}^3$. 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

Article information

Adv. Differential Equations, Volume 2, Number 3 (1997), 427-452.

First available in Project Euclid: 23 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q35: PDEs in connection with fluid mechanics
Secondary: 76D05: Navier-Stokes equations [See also 35Q30] 76W05: Magnetohydrodynamics and electrohydrodynamics


Gerbeau, J.-F.; Le Bris, C. Existence of solution for a density-dependent magnetohydrodynamic equation. Adv. Differential Equations 2 (1997), no. 3, 427--452.

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