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

2017/09/25 by Zhiqiang Shao, Shao, Zhiqiang
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1709.08445

openalex publication_date 2017/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Delta-Shock Waves as Limits of Vanishing Viscosity for Hyperbolic Systems of Conservation Laws

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