Symmetrizations of RMHD equations and stability of relativistic current–vortex sheets

We consider the equations of relativistic magnetohydrodynamics (RMHD) in the case of special relativity. Starting by computations in the fluid's rest frame and then applying Lorentz transformations, we derive a covariant symmetric formulation of RMHD in terms of the primitive (physical) variables. This symmetric system is important for the study of various initial boundary value problems. We also find a so-called secondary symmetrization whose direct consequence is the extension of the sufficient stability condition obtained earlier for non-relativistic planar current–vortex sheets to the relativistic case. As in non-relativistic settings, this implies the local-in-time existence of corresponding smooth nonplanar current–vortex sheets. (paper)