Smooth Subsonic and Transonic Flows with Nonzero Angular Velocity and Vorticity to steady Euler-Poisson system in a Concentric Cylinder

TL;DR

This paper establishes the existence and structural stability of smooth subsonic and transonic flows with nonzero angular velocity and vorticity in a steady Euler-Poisson system within a concentric cylinder, addressing hyperbolic-elliptic mixed structures.

Contribution

It proves the existence and stability of cylindrically symmetric flows with nonzero vorticity in a steady Euler-Poisson system, using a novel decomposition method.

Findings

Existence of smooth subsonic and transonic flows in a concentric cylinder.

Structural stability under perturbations for both flow types.

A priori estimates and uniqueness results for the elliptic system.

Abstract

In this paper, both smooth subsonic and transonic flows to steady Euler-Poisson system in a concentric cylinder are studied. We first establish the existence of cylindrically symmetric smooth subsonic and transonic flows to steady Euler-Poisson system in a concentric cylinder. On one hand, we investigate the structural stability of smooth cylindrically symmetric subsonic flows under three-dimensional perturbations on the inner and outer cylinders. On the other hand, the structural stability of smooth transonic flows under the axi-symmetric perturbations are examined. There is no any restrictions on the background subsonic and transonic solutions. A deformation-curl-Poisson decomposition to the steady Euler-Poisson system is utilized in our work to deal with the hyperbolic-elliptic mixed structure in subsonic region. It should be emphasized that there is a special structure of the steady Euler-Poisson system which yields a priori estimates and uniqueness of a second order elliptic system for the velocity potential and the electrostatic potential.