Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On stability of shock waves in relativistic magnetohydrodynamics


Author: Yu. L. Trakhinin
Journal: Quart. Appl. Math. 59 (2001), 25-45
MSC: Primary 76W05; Secondary 35L50, 35Q35, 76L05
DOI: https://doi.org/10.1090/qam/1811093
MathSciNet review: MR1811093
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Abstract: The structural stability of relativistic magnetohydrodynamic shock waves is studied. Stability results are obtained for the special case of fast parallel shock waves. It is proved that the instability and linear stability domains coincide with those of shock waves in relativistic gas dynamics. The domain of structural (nonlinear) stability, where the uniform Lopatinski condition is fulfilled for the stability problem, is found. It is shown that the structural stability domain is smaller than that of relativistic gas dynamic shock waves.


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DOI: https://doi.org/10.1090/qam/1811093
Article copyright: © Copyright 2001 American Mathematical Society


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