Two dimensional subsonic flows with self-gravitation in bounded domain
Analysis of PDEs
2014-06-18 v1
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.
Cite
@article{arxiv.1406.4255,
title = {Two dimensional subsonic flows with self-gravitation in bounded domain},
author = {Myoungjean Bae and Ben Duan and Chunjing Xie},
journal= {arXiv preprint arXiv:1406.4255},
year = {2014}
}