A potential lagrangian formulation of ideal MHD

We propose a reformulation of ideal magnetohydrodynamics written in the lagrangian variable as an enlarged system of hyperelastic type, with a specific potential. We study the hyperbolicity of the model and prove that the acoustic tensor is positive for all directions which are non orthogonal to the magnetic field. The consequences for eulerian ideal magnetohydrodynamics and for numerical discretization are briefly discussed at the end of this work.