Geometric Optics for Surface Waves on the Plasma–Vacuum Interface

We consider the free boundary problem for a plasma–vacuum interface in ideal incompressible magnetohydrodynamics, where the Maxwell equations for electric and magnetic fields are considered in the vacuum region. Under a necessary and sufficient stability condition for a piecewise constant background state, we construct approximate solutions at any arbitrarily large order of accuracy to the free boundary problem in three space dimensions when the initial discontinuity displays high frequency oscillations. Moreover, such approximate surface waves have nontrivial residual non-oscillatory components. The content of this paper summarizes the result in Secchi and Yuan (2022).