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Mathematical Methods for the Magnetohydrodynamics of Liquid Metals$
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Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre

Print publication date: 2006

Print ISBN-13: 9780198566656

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198566656.001.0001

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THE MAGNETOHYDRODYNAMICS EQUATIONS

THE MAGNETOHYDRODYNAMICS EQUATIONS

Chapter:
(p.1) 1 THE MAGNETOHYDRODYNAMICS EQUATIONS
Source:
Mathematical Methods for the Magnetohydrodynamics of Liquid Metals
Author(s):

Jean-Frédéric Gerbeau

Claude Le Bris

Tony Lelièvre

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198566656.003.0001

This chapter presents how MHD equations can be derived from the general conservation equations for fluid mechanics coupled with the Maxwell equations modelling the electromagnetic phenomena. A hierarchy of models is considered, from the most general one (a full time-dependent system consisting in the incompressible Navier-Stokes equations with a Lorentz body force calculated from the Maxwell equations and the Ohm's law) to the most simplified one. Depending on the physical context, one model or the other is appropriate. The most sophisticated model raises unsolved questions of existence and uniqueness, mainly related with the hyperbolic nature of the Maxwell equations, but some simpler models can be fully analysed.

Keywords:   multifluid flow, Maxwell equations, Navier-Stokes equations, MDH equations, Ohm's law, Lorentz body force

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