Riemann problem for a two‐dimensional steady pressureless relativistic Euler equations

Abstract

We consider the Riemann problem for a two‐dimensional steady pressureless relativistic Euler equations. The delta shock wave is discovered in the Riemann solutions. It is shown that Dirac delta function develops in the state variable describing the number density of particles. By virtue of a suitable generalized Rankine–Hugoniot relation and entropy condition, we establish the existence and uniqueness for delta‐shock solution. Furthermore, we analyze in detail the interactions of delta shock waves and vacuum states.