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In this paper, both smooth subsonic and transonic flows to steadyEuler-Poisson system in a concentric cylinder are studied. We first establishthe existence of cylindrically symmetric smooth subsonic and transonic flows tosteady Euler-Poisson system in a concentric cylinder. On one hand, weinvestigate the structural stability of smooth cylindrically symmetric subsonicflows under three-dimensional perturbations on the inner and outer cylinders.On the other hand, the structural stability of smooth transonic flows under theaxi-symmetric perturbations are examined. There is no any restrictions on thebackground subsonic and transonic solutions. A deformation-curl-Poissondecomposition to the steady Euler-Poisson system is utilized in our work todeal with the hyperbolic-elliptic mixed structure in subsonic region. It shouldbe emphasized that there is a special structure of the steady Euler-Poissonsystem which yields a priori estimates and uniqueness of a second orderelliptic system for the velocity potential and the electrostatic potential.

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