Delta shocks in the relativistic full Euler equations for a Chaplygin gas

Abstract

The relativistic full Euler equations for a Chaplygin gas are studied. The Riemann problem is solved constructively. There are two kinds of Riemann solutions, in which one consists of three contact discontinuities and the other involves a delta shock wave on which both state variables the rest mass density and the proper energy density simultaneously contain the Dirac delta functions. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. The formation mechanism, generalized Rankine-Hugoniot relation and entropy condition are clarified for this type of delta shock wave. Under the generalized Rankine-Hugoniot relation and entropy condition, the existence and uniqueness of delta shock solutions are also established.