Structural stability of smooth axisymmetric subsonic spiral flows with self-gravitation in a concentric cylinder

Abstract

This paper concerns the existence and stability of smooth axisymmetric subsonic spiral flows with self-gravitation in a concentric cylinder. Firstly, the existence and uniqueness of smooth cylindrically symmetric subsonic spiral flows with self-gravitation are proved. Then we establish the structural stability of this background subsonic flows under axisymmetric perturbations of suitable boundary conditions, which yields the existence and uniqueness of smooth axisymmetric subsonic spiral flows with nonzero angular velocity and vorticity to the steady self-gravitating Euler-Poisson system. By the stream function formulation, the steady Euler-Poisson system for the axisymmetric self-gravitating flows can be decomposed into a second-order nonlinear elliptic system coupled with several transport equations. The key ingredient of the analysis is to discover a special structure of the associated elliptic system for the stream function and the gravitational potential, which enable us to obtain a priori estimates for the linearized elliptic problem.