摘要
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.
出处
《应用数学》
CSCD
北大核心
2013年第1期146-154,共9页
Mathematica Applicata
基金
Supported by the Fundamental Research Funds for the Central Universities(2011-1a-021)
关键词
欧拉-泊松方程组
平衡解
正解
Euler-Poisson equation Stationary solution Positive solution