Anisotropic regularity of linearized compressible vortex sheets

Abstract

We consider supersonic vortex sheets for the Euler equations of compressible inviscid fluids in two space dimensions. For the problem with constant coefficients, Morando et al. recently derived a pseudo-differential equation that describes the time evolution of the discontinuity front of the vortex sheet. In agreement with the classical stability analysis, the problem is weakly stable if [Formula: see text], and the well-posedness holds in standard weighted Sobolev spaces. Our aim in this paper is to improve this result, by showing the existence in functional spaces with additional weighted anisotropic regularity in the frequency space.