Solutions with concentration and cavitation to the Riemann problem for the isentropic relativistic Euler system for the extended Chaplygin gas

Abstract

The solutions to the Riemann problem for the isentropic relativistic Euler system for the extended Chaplygin gas are constructed for all kinds of situations by using the method of phase plane analysis. The asymptotic limits of solutions to the Riemann problem for the relativistic extended Chaplygin Euler system are investigated in detail when the pressure given by the equation of state of extended Chaplygin gas becomes that of the pressureless gas. During the process of vanishing pressure, the phenomenon of concentration can be identified and analyzed when the two-shock Riemann solution tends to a delta shock wave solution as well as the phenomenon of cavitation also being captured and observed when the two-rarefaction-wave Riemann solution tends to a two-contact-discontinuity solution with a vacuum state between them.

Keywords

• isentropic relativistic euler system
• extended chaplygin gas
• pressureless fluid
• delta shock wave
• vacuum state
• riemann problem
• 35l65
• 35l67
• 76n15