Two-dimensional subsonic flows with self-gravitation in bounded domain

Abstract

We investigate two-dimensional steady Euler–Poisson system which describes the motion of compressible self-gravitating flows. The unique existence and stability of subsonic flows in a duct of finite length are obtained when prescribing the entropy at the entrance and the pressure at the exit. After introducing the stream function, the Euler–Poisson system can be decomposed into several transport equations and a second-order nonlinear elliptic system. We discover an energy estimate for the associated elliptic system which is a key ingredient to prove the unique existence and stability of subsonic flow.