Simplified variational principles for barotropic magnetohydrodynamics

Variational principles for magnetohydrodynamics were introduced by previous au- thors both in Lagrangian and Eulerian form. In a previous work Yahalom & Lynden-Bell intro- duced a simpler Eulerian variational principles from which all the relevant equations of magneto- hydrodynamics can be derived. The variational principle were 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 B the velocity field v and the density ρ. In this work I will attempt to improve on our previous results thus reducing the number of functions needed even further.