Cauchy problem with general discontinuous initial data along a smooth curve for 2-d Euler system

被引：12

作者：

Chen, Shuxing ^{[1
]}

Li, Dening ^{[2
]}

机构：

[1] Fudan Univ, Sch Mat Sci, Shanghai 200433, Peoples R China

[2] W Virginia Univ, Dept Math, Morgantown, WV 26506 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2014年 / 257卷 / 06期

关键词：

Cauchy problem; Euler systems; Discontinuous initial data; Shock; Rarefaction wave; Contact discontinuity; COMPRESSIBLE VORTEX SHEETS; 2 SPACE DIMENSIONS; CONSERVATION-LAWS; HYPERBOLIC SYSTEMS;

D O I：

10.1016/j.jde.2014.05.027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the Cauchy problems for the isentropic 2-d Euler system with discontinuous initial data along a smooth curve. All three singularities are present in the solution: shock wave, rarefaction wave and contact discontinuity. We show that the usual restrictive high order compatibility conditions for the initial data are automatically satisfied. The local existence of piecewise smooth solution containing all three waves is established. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：1939 / 1988

页数：50

共 29 条

[1]

Alinhac S., 1989, Commun. Partial Differ. Eqs., V14, P173

[2]

Ben-Dor G, 2007, SHOCK WAVE HIGH PRES, P1

[3]

Bezard M., 1990, J EQU DERIV PARTIELL, P1

[4] DOUBLE SHOCK FRONTS FOR HYPERBOLIC SYSTEMS OF CONSERVATION-LAWS IN MULTIDIMENSIONAL SPACE [J].

BUI, AT ;

LI, D .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 316 (01) :233-250

[5]

Chen S. X., P INT C MATH 2010 HY

[6]

CHEN SX, 1989, J DIFFER EQUATIONS, V80, P199, DOI 10.1016/0022-0396(89)90082-X

[7] EXISTENCE OF LOCAL SOLUTION TO SUPERSONIC-FLOW PAST A 3-DIMENSIONAL WING [J].

CHEN, SX .

ADVANCES IN APPLIED MATHEMATICS, 1992, 13 (03) :273-304

[8]

Coulombel JF, 2008, ANN SCI ECOLE NORM S, V41, P85

[9] UNIQUENESS OF 2-D COMPRESSIBLE VORTEX SHEETS [J].

Coulombel, Jean-Francois ;

Secchi, Paolo .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2009, 8 (04) :1439-1450

[10] The stability of compressible vortex sheets in two space dimensions [J].

Coulombel, JF ;

Secchi, P .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2004, 53 (04) :941-1012

← 1 2 3 →