This paper shows time-asymptotic nonlinear stability and existence of the viscous shock profiles to the Cauchy problem of the one-dimensional compressible planar magnetohydrodynamics system, which describes the motions of a conducting fluid in an electro-magnetohydrodynamics system. We can prove that the solutions to the compressible planar magnetohydrodynamics system tend time-asymptotically to the viscous shock profiles provided that the initial disturbance is small and of integral zero.
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The authors were supported by the National Natural Science Foundation of China (Grant Nos. 12071163 and 11601165) and Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (Grant No. ZQN-PY602).
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Ding, Q., Yin, H. Asymptotic stability of viscous shock profiles for compressible planar magnetohydrodynamics system. Z. Angew. Math. Phys. 72, 11 (2021). https://doi.org/10.1007/s00033-020-01431-4
- Planar magnetohydrodynamics system
- Shock profiles
- Asymptotic stability
Mathematics Subject Classification