Anisotropic regularity of linearized compressible vortex sheets

Paolo Secchi

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arXiv · 2008.05956

Anisotropic regularity of linearized compressible vortex sheets

Paolo Secchi

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Abstract

We are concerned with supersonic vortex sheets for the Euler equations of compressible inviscid fluids in two space dimensions. For the problem with constant coefficients, in [10] the authors have derived a pseudo-differential equation which 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 $|[v\cdot\tau]|>2\sqrt{2}\,c$, and the well-posedness was obtained in standard weighted Sobolev spaces. The aim of the present paper is to improve the result of [10], by showing the existence of the solution in function spaces with some additional weighted anisotropic regularity in the frequency space.

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Paolo Secchi. 2020-08-12. Anisotropic regularity of linearized compressible vortex sheets. https://arxiv.org/abs/2008.05956

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