The Existence of Current-Vortex Sheets in Ideal Compressible Magnetohydrodynamics

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Well-Posedness in Smooth Function Spaces for the Moving-Boundary Three-Dimensional Compressible Euler Equations in Physical Vacuum (2012, unknown): “This class of problems has been studied by [2,4,5,37,39] and others, and has the relative disadvantage of violating the uniform Kreiss–Lopatinskii condition, which produces derivative loss in the linearization, similar to that experienced by many authors in the incompressible flow setting (both irro”
Well‐posedness in smooth function spaces for moving‐boundary 1‐D compressible euler equations in physical vacuum (2009, result): “on-characteristic case, is the characteristic boundary case, encountered in the study of vortex sheet or current vortex sheet problems. This class of problems has been studied by [3], [5], [6], [38], [40] and others, and has the relative disadvantage of violating the uniform Kreiss–Lopatinskii condi”