Stability of composite wave for inflow problem on the planar magnetohydrodynamics

In this paper, we investigate the large time behavior of the solutions to an initial-boundary value problem for the planar magnetohydrodynamics in a half line R+≔(0,∞). Inspired by the relationship between magnetohydrodynamics and Navier-Stokes, we can prove that the composite wave consisting of the subsonic BL-solution, the contact wave, and the rarefaction wave for the inflow problem on the planar magnetohydrodynamics is time-asymptotically stable. Meanwhile, we obtain the global existence of solutions based on the basic energy method by taking into account the complexity of composite wave.