【摘要】 可压缩的欧拉-泊松方程组描述的是具有自引力势能的气态星体内部气体的运动发展规律,它由质量守恒方程、动量守恒方程、能量守恒方程及自引力位势满足的泊松方程构成.该文主要研究质量守恒和能量守恒的情况下方程组的平衡解.在绝热常数1<γ<6/5和熵函数满足一定的光滑性条件下,引用变量变换将方程组转化成一个半线性椭圆型方程,通过一个类似于Pohozaev等式的恒等式证明了平衡解的存在性.更多还原

【Abstract】 The compressible Euler-Poisson system,addressed to describe the time evolution of self-induced gravitational gaseous stars,consists of the Euler equations for the conservation of mass,momentum and energy,and Poisson equation induced by the potential function of the self-gravitational force.We consider stationary solutions of the Euler-Poisson equations,i.e.the solutions independent of time t,for some velocity fields and smooth entropy functions that solve the conservation of mass and energy.When 1 <γ<6/5 and the entropy function satisfies some smooth property,we introduce a nonlinear transformation to turn the Euler-Poisson system into a semilinear elliptic equation,and then obtain the existence of the stationary solutions by a similar Pohozaev’s identity proved in section 2.更多还原