Delta shocks and vacuum states in vanishing pressure limits of solutions to the relativistic Euler equations

Abstract

The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations are obtained constructively. There are two kinds of solutions, the one involves delta shock wave and the other involves vacuum. The authors prove that these two kinds of solutions are the limits of the solutions as pressure vanishes in the Euler system of conservation laws of energy and momentum in special relativity.

Keywords

Relativistic Euler equations in special relativity / Pressureless relativistic Euler equations / Delta shock waves / Vacuum / Vanishing pressure limits

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