Anisotropic regularity of linearized compressible vortex sheets
| Autor: | Secchi, Paolo |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 14 pages. To appear in J. Hyperbolic Differ. Equ. arXiv admin note: substantial text overlap with arXiv:1806.06740 |
| Databáze: | arXiv |
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