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Local Existence of Contact Discontinuities in Relativistic Magnetohydrodynamics
Siberian Advances in Mathematics Pub Date : 2020-03-17 , DOI: 10.3103/s1055134420010058
Yu. L. Trakhinin

We study the free boundary problem for a contact discontinuity for the system of relativistic magnetohydrodynamics. A surface of contact discontinuity is a characteristic of this system with no flow across the discontinuity for which the pressure, the velocity and the magnetic field are continuous whereas the density, the entropy and the temperature may have a jump. For the two-dimensional case, we prove the local-in-time existence in Sobolev spaces of a unique solution of the free boundary problem provided that the Rayleigh-Taylor sign condition on the jump of the normal derivative of the pressure is satisfied at each point of the initial discontinuity.

中文翻译:

相对论磁流体动力学中接触间断的局部存在

我们研究了相对论磁流体动力学系统接触不连续的自由边界问题。接触不连续性的表面是该系统的特征,在该不连续性上没有流动,压力,速度和磁场是连续的,而密度,熵和温度可能会跳跃。对于二维情况,我们证明了在Sobolev空间中的时间局部存在的自由边界问题的唯一解,只要满足每个压力正态导数跃迁的Rayleigh-Taylor符号条件初始不连续点。
更新日期:2020-03-17
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