Stability of Riemann solutions with large oscillation for the relativistic Euler equations (Q1881153)

Entropy solutions of the \(2\times 2\) relativistic Euler equations are considered for perfect fluids in special relativity. The existence of Riemann solutions is established for a class of entropy solutions with arbitrarily large oscillations. The uniqueness of the Riemann solutions then yields their inviscid large-time stability with respect to arbitrarily large perturbations of the initial Riemann data. Finally, an extension is made to show the stability and uniqueness of vacuum Riemann solutions in a class of entropy solutions with arbitrarily large oscillations.