中文摘要：

对于等温气体,作者将考虑具有球对称结构的相对论欧拉方程组经典稳态解（定理1.1）和弱稳态解（定理1.2）的存在性.通过求解两个常微分方程以及比较马赫数M和1的关系,定理1.1证明了相对论欧拉方程组经典稳态解的存在性.在一个C^2,α,α∈（0,1）稳态背景解的扰动下,定理1.2将证明高维球对称跨音速（双曲-椭圆）解的存在性.

英文摘要：

In this paper, for isothermal gas, we will think about the existence of classical （Theorem 1.1） and weak （Theorem 1.2） solutions of steady state relativistic Euler equations with spherical symmetry structure, respectively. Theorem 1.1 shows that, by solving two or- dinary differential equations and according to the comparison of Mach number M and 1, we establish the existence of classical solutions. Moreover, Theorem 1.2 shows that, under a C^2＇a, a c （0,1） steady perturbation of the upstream supersonic flow, we will prove the existence of steady multidimensional transonic shocks （hyperbolic-elliptic shocks） for spherically symmetric relativistic Euler equations.