可压缩欧拉-泊松方程组平衡解的存在性(英文)

On the Existence of Stationary Solutions of the Compressible Euler-Poisson Equations

可压缩欧拉-泊松方程组描述的是具自引力势能气态星体内部气体的运动变化.对于满足质量守恒和能量守恒的一些速度场,本文在熵函数的光滑性较弱的条件下研究欧拉-泊松方程组平衡解的存在性.在本文中,作者应用变分方法得到6/5<γ<2时方程组平衡解的存在性结果.该结果减弱了关于非旋转星体欧拉-泊松方程组平衡解存在的条件,从而适用于更一般的物理环境.

The time evolution of the self-induced gravitational gaseous stars can be modeled by the compressible Euler-Poisson equations. For 6/5〈r〈 2, by the variational method, we study the ex- istence of stationary solutions for some velocity fields that solve the conservation of mass and ener- gy, with weak smoothness of entropy functions. Our result improves the previous works on the irro- tational gaseous stars,and then it holds in more general physical settings.