1202.1946 (Heinrich Freistühler et al.)

Symmetrizations of RMHD equations and stability of relativistic
current-vortex sheets    [PDF]

Heinrich Freistühler, Yuri Trakhinin

We consider the equations of relativistic magnetohydrodynamics (RMHD) in the
case of special relativity. For the fluid rest frame a nonconservative
reformulation of the RMHD equations gives a symmetric system for the vector of
primitive (physical) variables. By applying the Lorentz transformation to this
system we find a concrete form of symmetric matrices in the LAB-frame. The
resulting symmetric system in terms of primitive variables is important for the
study of various initial boundary value problems for the RMHD equations. 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.

View original: http://arxiv.org/abs/1202.1946