Relativistic Euler equations for isentropic fluids: stability of Riemann solutions with large oscillation (Q1764414)

The authors study the global entropy solutions of \(2\times 2 \) relativistic Euler equations for isentropic fluids in special relativity. The study is focused on the uniqueness of Riemann solutions in the class \(L^{\infty }\cap BV_{loc} \). These are entropy solutions with arbitrarily large oscillation. The uniqueness of the Riemann solutions implies their inviscid time-asymptotic stability under arbitrarily large \(L^{ 1 }\cap L^{\infty }\cap BV_{loc}\) perturbation of the Riemann initial data, provided that the corresponding solutions are in \(L^{\infty }\) and have local bounded total variation that allows the linear growth in time. The stability of the entropy solutions containing vacuum in the class \(L^{\infty }\) is discussed as well.