关于相对论理想磁流体力学的凸性
On the convexity of Relativistic Ideal Magnetohydrodynamics
摘要：
分析了磁场对相对论磁流体力学方程组凸性的影响。为此，我们使用的方法的拉克斯，基于分析的线性退化/真正的非线性性质的特征字段。分别讨论了简并态和非简并态，并适当地恢复了非相对论性、非磁化极限。对应于物质波和阿尔文波的特征场是线性退化的，因此不受凸性问题的影响。然而，与磁声波相关的特征场的分析揭示了凸性条件对磁场的依赖性。结果表示为一个广义基本导数的形式写为两项之和。第一个是广义基本导数的情况下，纯流体动力学（相对论）流。第二个包含了磁场的影响。对该项的分析表明，它总是正的，从而导致流体中磁场的存在减小了状态方程非凸的热力学状态域的显著结果。
英文摘要：
We analyze the influence of the magnetic field in the convexity properties of the relativistic magnetohydrodynamics system of equations. To this purpose we use the approach of Lax, based on the analysis of the linearly degenerate/genuinely non-linear nature of the characteristic fields. Degenerate and non-degenerate states are discussed separately and the non-relativistic, unmagnetized limits are properly recovered. The characteristic fields corresponding to the material and Alfvén waves are linearly degenerate and, then, not affected by the convexity issue. The analysis of the characteristic fields associated with the magnetosonic waves reveals, however, a dependence of the convexity condition on the magnetic field. The result is expressed in the form of a generalized fundamental derivative written as the sum of two terms. The first one is the generalized fundamental derivative in the case of purely hydrodynamical (relativistic) flow. The second one contains the effects of the magnetic field. The analysis of this term shows that it is always positive leading to the remarkable result that the presence of a magnetic field in the fluid reduces the domain of thermodynamical states for which the EOS is non-convex.
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