Delta waves of the isentropic relativistic Euler system coupled with an advection equation for Chaplygin gas

Abstract

Abstract Most previous studies concerning delta waves have been focused on the overcompressible ones. To study the non-overcompressible delta waves, this article is concerned with the isentropic relativistic Euler system coupled with an advection equation for Chaplygin gas. The Riemann problem is completely solved. The solutions exhibit four kinds of wave patterns: the first contains three contact discontinuities; the second includes a single overcompressible delta wave, and the third and fourth involve a contact discontinuity and a non-overcompressible delta wave.