Shock-Free Solutions of the Compressible Euler Equations

被引：11

作者：

Chen, Geng ^{[1
]}

Young, Robin ^{[2
]}

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2015年 / 217卷 / 03期

关键词：

PARTIAL-DIFFERENTIAL-EQUATIONS; HYPERBOLIC SYSTEMS; WAVE-PROPAGATION; SMOOTH SOLUTIONS; GAS-DYNAMICS; SINGULARITIES; FLUIDS;

D O I：

10.1007/s00205-015-0854-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the structure of shock-free solutions of the compressible Euler equations with large data. We describe conditions under which the rarefactive/ compressive character of solutions changes, and conditions under which the vacuum is formed asymptotically. We present several new examples of shock-free solutions, which demonstrate a large variety of behaviors.

引用

页码：1265 / 1293

页数：29

共 37 条

[1] Bressan A., 2000, ONE DIMENSIONAL CAUC, V20
[2] Chang T., 1989, Pitman Monographs and Surveys in Pure and Applied Mathematics, V41
[3] CHEN G., 2010, THESIS U MASSACHUSET
[4] CHEN G., 2014, PREPRINT
[5] SHOCK FORMATION IN THE COMPRESSIBLE EULER EQUATIONS AND RELATED SYSTEMS
Chen, Geng
Young, Robin
Zhang, Qingtian
[J]. JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2013, 10 (01) : 149 - 172
[6] FORMATION OF SINGULARITY AND SMOOTH WAVE PROPAGATION FOR THE NON-ISENTROPIC COMPRESSIBLE EULER EQUATIONS
Chen, Geng
[J]. JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2011, 8 (04) : 671 - 690
[7] Smooth solutions and singularity formation for the inhomogeneous nonlinear wave equation
Chen, Geng
Young, Robin
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (03) : 2580 - 2595
[8] Courant R., 1976, Supersonic Flow and Shock Waves, V21
[9] Dafermos C.M., 2010, HYPERBOLIC CONSERVAT, VVolume 325, pXXXVI+708
[10] SOLUTIONS IN LARGE FOR NONLINEAR HYPERBOLIC SYSTEMS OF EQUATIONS
GLIMM, J
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1965, 18 (04) : 697 - &

← 1 2 3 4 →