中文摘要：

三维可压等熵欧拉泊松方程组描述可压等熵理想气态星体的运动规律，它由质量守恒方程、动量守恒方程及自引力位势满足的泊松方程构成。研究欧拉泊松方程组的自相似解是天体物理及数学领域研究的热点问题之一，具有重要的现实意义和广阔的应用前景。关于三维可压等熵欧拉泊松方程组自相似解的研究较少。用分离变量法研究了一类三维可压等熵欧拉泊松方程组的一组自相似解。

英文摘要：

The isentropic compressible Euler-Poisson equations,addressed to describe the motion of ide-al gaseous stars,consist of the Euler-Poisson equations for the conservation of mass and momentum,and Poisson equation induced by the potential function of the self-gravitational force.Using the separation method,self-similar solution are presented for the isentropic compressible Euler-Poisson equations in three dimension.