Nonlinear stability of rarefaction waves for the compressible MHD equations.

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 , θ 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 β = v + b + is bounded by a specific constant. The proof of the main result is based on elementary L 2 energy methods. [ABSTRACT FROM AUTHOR]