Nonlinear stability of rarefaction waves for the compressible MHD equations

作者：Yao, Huancheng^*; Zhu, Changjiang

来源：Zeitschrift für Angewandte Mathematik und Physik, 2023, 74(4): 137.

DOI：10.1007/s00033-023-02024-7

• The compressible non-isentropic MHD equations
• Rarefaction wave
• Nonlinear stability

This paper is concerned with time-asymptotic nonlinear stability of rarefaction waves to the Cauchy problem for one-dimensional compressible non-isentropic magnetohydrodynamics (MHD) equations (including its isentropic case), which describe the motion of a conducting fluid in a magnetic field. Through some elaborate and rigorous mathematical analysis, we can construct the rarefaction waves (v(r), u(r), theta(r), b(r)) (x/t) where magnetic component b(r) (x/t) is a nontrivial profile, namely a non-constant function. Then the solution of the compressible MHD equations is proved to tend towards the rarefaction waves time-asymptotically under small initial perturbations and weak wave strength, and also under a technical assumption that the parameter beta = v(+)b(+) is bounded by a specific constant. The proof of the main result is based on elementary L-2 energy methods.

• 单位
  华南农业大学