Riemann problem for the relativistic Chaplygin Euler equations

The relativistic Euler equations for a Chaplygin gas are studied. The Riemann problem is solved constructively. There are five kinds of Riemann solutions, in which four only contain different contact discontinuities and the other involves delta shock waves. Under suitable generalized Rankine–Hugonio...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 381; no. 1; pp. 17 - 26
Main Authors Cheng, Hongjun, Yang, Hanchun
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.09.2011
Elsevier
Subjects
Chaplygin gas
Delta shock wave
Exact sciences and technology
Generalized Rankine–Hugoniot relation
Linearly degenerate
Mathematical analysis
Mathematics
Partial differential equations
Relativistic Euler equations
Sciences and techniques of general use
Delta shock wave
Generalized Rankine–Hugoniot relation
Linearly degenerate
Relativistic Euler equations
Chaplygin gas
Solution uniqueness
Euler equation
Existence condition
Riemann problem
Mathematical analysis
Generalized Rankine-Hugoniot relation
Entropy
Shock wave
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Summary:The relativistic Euler equations for a Chaplygin gas are studied. The Riemann problem is solved constructively. There are five kinds of Riemann solutions, in which four only contain different contact discontinuities and the other involves delta shock waves. Under suitable generalized Rankine–Hugoniot relation and entropy condition, the existence and uniqueness of delta-shock solutions are established.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2011.04.017