Abstract
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.
Highlights
It is very important to understand the relativistic uid dynamics in the study of various astrophysical phenomena [1], such as the gravitational collapse, the supernova explosion and the formation and acceleration of the universe
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
Summary
It is very important to understand the relativistic uid dynamics in the study of various astrophysical phenomena [1], such as the gravitational collapse, the supernova explosion and the formation and acceleration of the universe. There exists a vast amount of literature in various models of relativistic uid dynamics since the fundamental work of Taub [2]. Only a few analytical theories have been developed such as in [3,4,5,6] due to the complicated structures of various relativistic uid dynamics models. In this present work, we draw our attention on the isentropic Euler system of two conservation laws consisting of energy and momentum in special relativity in the following form [3, 5,6,7].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
