Isentropic Approximation Of Cauchy Problem Of The One Dimension Relative Euler System

In this article,we study the approximate solution of one dimension relativistic Eu-ler equations derived from relativistic Boltzmann equations.The applied constitutive equations are different from common ones but involve modified Bessel functions of the second kind and this makes relativistic Euler equations rather complex.Based on deli-cate estimates of the Bessel functions,we study the structure of relativistic Euler equa-tions,then analyse their Riemann solutions.Using approximate solutions of relativistic Euler equations and their isentropic form constructed by wave-front tracking method,we apply the standard semigroup theory to compare Riemann solutions of approximate solutions,and further employ a semigroup formula to establish the approximation of two solutions of both relativistic Euler equations and its isentropic form on same isentropic initial data.