The ultra-relativistic Euler equations

We study the ultra‐relativistic Euler equations for an ideal gas, which is a system of nonlinear hyperbolic conservation laws. We first analyze the single shocks and rarefaction waves and solve the Riemann problem in a constructive way. Especially, we develop an own parametrization for single shocks...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2015-05, Vol.38 (7), p.1247-1264
Main Authors: Abdelrahman, Mahmoud A.E., Kunik, Matthias
Format: Article
Language:English
Subjects:
Conservation laws
Construction
entropy conditions
Euler equations
Eulers equations
hyperbolic system
Hyperbolic systems
Lorentz transformations
Mathematical analysis
Nonlinearity
Rarefaction
rarefaction waves
relativistic Euler equations
Riemann solutions
Shock fronts
shock waves
Uniqueness
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Summary:We study the ultra‐relativistic Euler equations for an ideal gas, which is a system of nonlinear hyperbolic conservation laws. We first analyze the single shocks and rarefaction waves and solve the Riemann problem in a constructive way. Especially, we develop an own parametrization for single shocks, which will be used to derive a new explicit shock interaction formula. This shock interaction formula plays an important role in the study of the ultra‐relativistic Euler equations. One application will be presented in this paper, namely, the construction of explicit solutions including shock fronts, which gives an interesting example for the non‐backward uniqueness of our hyperbolic system. Copyright © 2014 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.3141