Two dimensional subsonic flows with self-gravitation in bounded domain

2014/06/17 by Myoungjean Bae, Bae, Myoungjean, Ben Duan +3 · 2 citations
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1406.4255

openalex publication_date 2014/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Supersonic Euler-Poisson flows with nonzero vorticity in convergent nozzles
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