关键词: 欧拉-泊松方程组, 平衡解, 存在性

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.

Key words: Euler-Poisson equations, Stationary solutions, Existence