Advances in Differential Equations

Existence of solution for a density-dependent magnetohydrodynamic equation

J.-F. Gerbeau and C. Le Bris

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Abstract

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

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

Dates
First available in Project Euclid: 23 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366742251

Mathematical Reviews number (MathSciNet)
MR1441851

Zentralblatt MATH identifier
1023.35524

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

Citation

Gerbeau, J.-F.; Le Bris, C. Existence of solution for a density-dependent magnetohydrodynamic equation. Adv. Differential Equations 2 (1997), no. 3, 427--452. https://projecteuclid.org/euclid.ade/1366742251.


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