The ultra-relativistic Euler equations

摘要

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 (c) 2014 John Wiley & Sons, Ltd.