Two dimensional subsonic flows with self-gravitation in bounded domain

TL;DR

This paper studies the existence and stability of two-dimensional subsonic flows with self-gravitation in a bounded domain, using a decomposition into transport and elliptic equations and establishing energy estimates.

Contribution

It introduces a novel approach to prove unique existence and stability of subsonic self-gravitating flows in a finite duct by decomposing the Euler-Poisson system.

Findings

Proved unique existence of subsonic flows under given boundary conditions.

Established stability of these flows.

Developed an energy estimate for the elliptic system involved.

Abstract

We investigate two dimensional steady Euler-Poisson system which describe 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.