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A Four Function Variational Principle for Barotropic Magnetohydrodynamics

Asher Yahalom
Arxiv ID: 0811.2309Last updated: 2/12/2020
Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. In a previous work Yahalom Lynden-Bell introduced a simpler Eulerian variational principles from which all the relevant equations of magnetohydrodynamics can be derived. The variational principle was given in terms of six independent functions for non-stationary flows and three independent functions for stationary flows. This is less then the seven variables which appear in the standard equations of magnetohydrodynamics which are the magnetic field B⃗ the velocity field v⃗ and the density ρ. In this work I will improve on the previous results showing that non-stationary magnetohydrodynamics should be described by four functions .

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