| Abstract: |
| In this talk, we will introduce our recent results on the nonlinear stability of viscous contact wave for the isentropic compressible magnetohydrodynamics (MHD) equations with a free boundary. It is shown that when time tends to infinity, the fluid part of solutions will asymptotically converge to the viscous contact waves, and more importantly, the magnetic field will converge to a nontrivial wave pattern. This wave phenomenon is different from those of isentropic compressible Navier-Stokes equations, which means the magnetic field truly makes an essential effect on the fluid behavior. The main result is proved by using elaborate wave pattern analysis and elementary energy methods, provided the initial perturbations and wave strength are suitably small. |
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