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

TL;DR

This paper develops a symmetric formulation of relativistic magnetohydrodynamics equations, extending stability conditions for current-vortex sheets from non-relativistic to relativistic regimes, facilitating analysis of boundary value problems.

Contribution

It introduces a symmetric system for RMHD in the lab frame and extends stability criteria for current-vortex sheets to relativistic flows.

Findings

Derived a symmetric form of RMHD equations in the lab frame.

Extended stability conditions for current-vortex sheets to relativistic case.

Proved local-in-time existence of smooth nonplanar current-vortex sheets.

Abstract

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.