Riemann problem for the relativistic generalized Chaplygin Euler equations

Abstract

The Riemann problem for the relativistic generalized Chaplygin Euler equations is considered. Its two characteristic fields are genuinely nonlinear, but the nonclassical solutions appear. The formation of mechanism for $\delta-$shock is analyzed, that is the one-shock curve and the two-shock curve do not intersect each other in the phase plane. The Riemann solutions are constructed, and the generalized Rankine-Hugoniot conditions and the $\delta-$entropy condition are clarified. Moreover, under the generalized Rankine-Hugoniot conditions and entropy condition, we constructively obtain $\delta-$shock waves.