Stability and non-relativistic limits of rarefaction wave to the 1-D piston problem for the relativistic Euler equations

Abstract

We study the 1-D piston problem for the relativistic Euler equations under the assumption that the total variations of both the initial data and the velocity of the piston are sufficiently small. By a modified wave front tracking method, we establish the global existence of entropy solutions including a strong rarefaction wave without restriction on the strength. Meanwhile, we consider the convergence of the entropy solutions to the corresponding entropy solutions of the classical non-relativistic Euler equations as the light speed \(c\rightarrow +\infty \).