3-D axisymmetric subsonic flows with nonzero swirl for the compressible Euler-Poisson system

TL;DR

This paper establishes the structural stability of 3-D axisymmetric subsonic flows with nonzero swirl in the Euler-Poisson system by introducing a Helmholtz decomposition and analyzing a related elliptic system.

Contribution

It introduces a novel Helmholtz decomposition for axisymmetric flows with swirl and derives a quasilinear elliptic system to study stability.

Findings

Proves stability of subsonic flows with swirl under boundary conditions.

Develops a new mathematical framework for analyzing Euler-Poisson flows.

Addresses solvability issues related to the angular component of vorticity.

Abstract

We address the structural stability of 3-D axisymmetric subsonic flows with nonzero swirl for the steady compressible Euler-Poisson system in a cylinder supplemented with non small boundary data. A special Helmholtz decomposition of the velocity field is introduced for 3-D axisymmetric flow with a nonzero swirl(=angular momentum density) component. With the newly introduced decomposition, a quasilinear elliptic system of second order is derived from the elliptic modes in Euler-Poisson system for subsonic flows. Due to the nonzero swirl, the main difficulties lie in the solvability of a singular elliptic equation which concerns the angular component of the vorticity in its cylindrical representation, and in analysis of streamlines near the axis $r=0$.