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arXiv · 1202.1946

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

Heinrich Freistühler·Yuri Trakhinin
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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.

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Heinrich Freistühler, Yuri Trakhinin. 2012-02-09. Symmetrizations of RMHD equations and stability of relativistic current-vortex sheets. https://doi.org/10.1088/0264-9381/30/8/085012

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