Smooth Subsonic and Transonic Spiral Flows with Nonzero Vorticity to Steady Euler–Poisson System in Concentric Cylinders

Abstract

Both smooth subsonic and transonic spiral flows to steady Euler–Poisson system with nonzero angular velocity and vorticity in a concentric cylinder are studied. On the 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 is examined. There are no any restrictions on the background subsonic and transonic solutions. A deformation-curl-Poisson decomposition to the steady Euler–Poisson system is utilized to deal with the hyperbolic-elliptic mixed structure in the subsonic region. We emphasize that there is a special structure of the steady Euler–Poisson system which yields a priori estimates and uniqueness of the linearized elliptic system.