RMHD方程的对称化与相对论性流涡面的稳定性
Symmetrizations of RMHD equations and stability of relativistic current-vortex sheets
摘要：
本文考虑狭义相对论情形下的相对论磁流体力学方程。对于流体静止框架的非保守的RMHD方程的重新给出了一个对称系统的原始（物理）变量的矢量。通过对该系统进行洛伦兹变换，我们得到了在LAB-标架中对称矩阵的一种具体形式。由此得到的关于原始变量的对称系统对于研究RMHD方程的各种初边值问题是重要的。我们还发现了一个所谓的二次对称化，其直接后果是较早获得的非相对论平面电流涡片的相对论情况下的充分稳定性条件的延伸。在非相对论的设置，这意味着当地的时间存在相应的光滑的非平面电流涡面。
英文摘要：
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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