Stability of composite wave for inflow problem on the planar magnetohydrodynamics. (December 2018) - Yin, Haiyan
Abstract: 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.