Uniqueness of rarefaction waves in multidimensional compressible Euler system

被引：33

作者：

Feireisl, Eduard ^{[1
]}

Kreml, Ondrej ^{[1
]}

机构：

[1] Acad Sci Czech Republic, Inst Math, CR-11567 Prague 1, Czech Republic

来源：

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS | 2015年 / 12卷 / 03期

基金：

欧洲研究理事会;

关键词：

Compressible Euler system; uniqueness; rarefaction wave; Riemann problem; WEAK-STRONG UNIQUENESS; RIEMANN SOLUTIONS; GAS-DYNAMICS; BALANCE LAWS; EQUATIONS; STABILITY; FIELDS;

D O I：

10.1142/S0219891615500149

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that 1D rarefaction wave solutions are unique in the class of bounded entropy solutions to the multidimensional compressible Euler system. Such a result may be viewed as a counterpart of the recent examples of non-uniqueness of the shock wave solutions to the Riemann problem, where infinitely many solutions are constructed by the method of convex integration.

引用

页码：489 / 499

页数：11

共 15 条

[1] From kinetic equations to multidimensional isentropic gas dynamics before shocks [J].

Berthelin, F ;

Vasseur, A .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2005, 36 (06) :1807-1835

[2] Vanishing viscosity solutions of nonlinear hyperbolic systems [J].

Bianchini, S ;

Bressan, A .

ANNALS OF MATHEMATICS, 2005, 161 (01) :223-342

[3]

CHANG T., 1989, The Riemann Problem and Interaction of Waves in Gas Dynamics

[4] Uniqueness and asymptotic stability of Riemann solutions for the compressible Euler equations [J].

Chen, GQ ;

Frid, H .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 353 (03) :1103-1117

[5] Uniqueness and stability of Riemann solutions with large oscillation in gas dynamics [J].

Chen, GQ ;

Frid, H ;

Li, YC .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2002, 228 (02) :201-217

[6] On the theory of divergence-measure fields and its applications [J].

Chen, GQ ;

Frid, H .

BOLETIM DA SOCIEDADE BRASILEIRA DE MATEMATICA, 2001, 32 (03) :401-433

[7] Gauss-Green Theorem for Weakly Differentiable Vector Fields, Sets of Finite Perimeter, and Balance Laws [J].

Chen, Gui-Qiang ;

Torres, Monica ;

Ziemer, William P. .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2009, 62 (02) :242-304

[8] Global Ill-Posedness of the Isentropic System of Gas Dynamics [J].

Chiodaroli, Elisabetta ;

De Lellis, Camillo ;

Kreml, Ondrej .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2015, 68 (07) :1157-1190

[9] On the Energy Dissipation Rate of Solutions to the Compressible Isentropic Euler System [J].

Chiodaroli, Elisabetta ;

Kreml, Ondrej .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2014, 214 (03) :1019-1049

[10]

DAFERMOS CM, 1979, ARCH RATION MECH AN, V70, P167, DOI 10.1007/BF00250353

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