UNIQUENESS OF 2-D COMPRESSIBLE VORTEX SHEETS

被引：17

作者：

Coulombel, Jean-Francois ^{[1
,2
]}

Secchi, Paolo ^{[3
]}

机构：

[1] Univ Lille 1, CNRS, F-59655 Villeneuve Dascq, France

[2] INRIA Lille Nord Europe, Team Project SIMPAF, Lab Paul Painleve, F-59655 Villeneuve Dascq, France

[3] Univ Brescia, Fac Ingn, Dipartimento Matemat, I-25133 Brescia, Italy

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2009年 / 8卷 / 04期

关键词：

Compressible Euler equations; vortex sheets; contact discontinuities; weak Lopatinskii condition; loss of derivatives; 2 SPACE DIMENSIONS; HYPERBOLIC SYSTEMS; RAREFACTION WAVES; STABILITY;

D O I：

10.3934/cpaa.2009.8.1439

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider compressible vortex sheets for the isentropic Euler equations of dynamics in two space dimensions. Under a supersonic condition that precludes violent instabilities, in previous papers [3, 4] we have studied the linearized stability and proved the local existence of piecewise smooth solutions to the nonlinear problem. This is a free boundary nonlinear hyperbolic problem with two main difficulties: the free boundary is characteristic, and the so-called Lopatinskii condition holds only in a weak sense, which yields losses of derivatives. In the present paper we prove that sufficiently smooth solutions are unique.

引用

页码：1439 / 1450

页数：12

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