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.

中文翻译：

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二维稳态无压相对论欧拉方程的黎曼问题

我们考虑二维稳态无压相对论欧拉方程的黎曼问题。δ 激波是在黎曼解中发现的。结果表明，Dirac delta 函数在描述粒子数密度的状态变量中发展。凭借合适的广义Rankine-Hugoniot关系和熵条件，我们建立了delta-shock解的存在唯一性。此外，我们详细分析了 delta 冲击波和真空状态的相互作用。