SELF-SIMILAR SOLUTIONS OF THE SPHERICALLY SYMMETRIC EULER EQUATIONS FOR GENERAL EQUATIONS OF STATE

被引：0

作者：

Chen, Jianjun ^{[1
]}

Lai, Geng ^{[2
]}

机构：

[1] Zhejiang Univ Sci & Technol, Dept Math, Hangzhou 310023, Peoples R China

[2] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2021年 / 19卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Compressible Euler equations; van der Waals gas; spherical symmetry; self-similar solution; RIEMANN PROBLEM; AXISYMMETRICAL SOLUTIONS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The study of spherically symmetric motion is important for the theory of explosion waves. In this paper, we construct rigorously self-similar solutions to the Riemann problem of the spherically symmetric Euler equations for general equations of state. We use the assumption of self-similarity to reduce the spherically symmetric Euler equations to a system of nonlinear ordinary differential equations, from which we obtain detailed structures of solutions besides their existence.

引用

页码：1991 / 2018

页数：28

共 19 条

[1] Global solutions to the compressible Euler equations with geometrical structure
Chen, GQ
Glimm, J
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1996, 180 (01) : 153 - 193
[2] Remarks on spherically symmetric solutions of the compressible Euler equations
Chen, GQ
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1997, 127 : 243 - 259
[3] Vanishing Viscosity Solutions of the Compressible Euler Equations with Spherical Symmetry and Large Initial Data
Chen, Gui-Qiang G.
Perepelitsa, Mikhail
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2015, 338 (02) : 771 - 800
[4] Courant R., 1948, Supersonic Flow and Shock Waves
[5] Ding M., 2014, HYPERBOLIC CONSERVAT, V49, P161
[6] Godlewski E, 2006, COMMUN MATH SCI, V4, P227
[7] Axisymmetric solutions of the two-dimensional Euler equations with a two-constant equation of state
Hu, Yanbo
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2014, 15 : 67 - 79
[8] Jenssen HK, 2011, IMA VOL MATH APPL, V153, P331
[9] LeFloch P.G, 2002, LECT MATH ETH ZURICH
[10] Finite energy solutions to the isentropic Euler equations with geometric effects
LeFloch, Philippe G.
Westdickenberg, Michael
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 88 (05): : 389 - 429

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