Riemann problem with delta initial data for the isentropic relativistic Chaplygin Euler equations

• DOI: 10.1007/s00033-016-0663-x
• Publication Date: 2016-05-12T05:28:25Z
• Authors: Zhiqiang Shao
• Keywords: Isentropic process; Dirac delta function; Chaplygin gas; Euler system

In this paper, we study the Riemann problem with the initial data containing the Dirac delta function for the isentropic relativistic Chaplygin Euler equations. Under suitably generalized Rankine–Hugoniot relation and entropy condition, we constructively obtain the global existence of generalized solutions including delta shock waves that explicitly exhibit four kinds of different structures. Moreover, it can be found that the solutions constructed here are stable for the perturbation of the initial data.