The Limit Problem Of The Riemann Solution For The Isentropic Relativistic Euler System

In our work,we mainly pay attention to investigating the extended Chaplygin gas for the isentropic relativistic Euler system that the equation of state is the third-order and second-order form and the two different perturbed macroscopic production models.Firstly,we shall focus on the Riemann problems of four kinds of equations.The Riemann solutions of four kinds of equations are constructed for all the possible cases by using the method of phase plane analysis.Then,the limits of equations can be studied by the vanishing pressure method.Specifically,we shall first consider the asymptotic limits of the Riemann solutions for the relativistic Euler equations when the equation of state of extended Chaplygin gas becomes the one of pressureless gas.Secondly,the asymptotic limits of solutions to the Riemann problem for the relativistic Euler equations are captured when the equation of state of extended Chaplygin gas becomes the one of Chaplygin gas.Finally,we draw our attention on the asymptotic limits relations of the Riemann solutions for the two different perturbed macroscopic production models and pressureless gas dynamics model.The organization of article is planed as followsIn chapter one,the background and development of the status of the isentropic relativistic Euler system and the macroscopic production model are introduced.In chapter two,the basic concepts and correlation theory that is related to the studying contents are given.In chapter three,the Riemann solutions of the isentropic relativistic Euler system for the extended Chaplygin gas are considered.Then,we will mainly discuss the relation of Riemann solutions for the isentropic relativistic Euler system when the equation of state of extended Chaplygin gas becomes the one of pressureless gas.To be exact,when the limit A1,A2,A3,B?0 is taken in the Riemann solutions of the isentropic relativistic Euler system for the extended Chaplygin gas,the formation of delta shock wave and two-contact-discontinuity with a vacuum state between them are captured,which is identical with the Riemann solutions for the zero-pressure relativistic Euler system.In chapter four,the Riemann solutions of the isentropic relativistic Euler system for the extended Chaplygin gas are investigated.Then,we will mainly discuss the relation of Riemann solutions for the isentropic relativistic Euler system when the equation of state of extended Chaplygin gas becomes the one of Chaplygin gas.To be more specific,when the limit A1,A2?0 is taken in the Riemann solutions of the isentropic relativistic Euler system for the extended Chaplygin gas,the formation of delta shock wave and two-contact-discontinuity can be identified,which is identical with the Riemann solutions of the isentropic relativistic Euler system for the Chaplygin gas.In chapter five,the solutions of the Riemann problem for the perturbed macroscopic production model are investigated.In addition,we consider the firstly kind of perturbed macroscopic production model.Delta shock wave and two-contact-discontinuity are formed as ??0,which are different from the corresponding Riemann solutions of the pressureless gas dynamics model.Because the delta shock wave in the limit situation has different propagation speed and strength from those for the pressureless gas dynamics model.Then,when the limit ??0 is taken in the second kind of perturbed macroscopic production model,the formation of delta shock wave and two-contact-discontinuity is analyzed,whose asymptotic limits of Riemann solutions are identical with those of the pressureless gas dynamics model.