  In this paper, we are concerned with the global existence and stability of a
3-D perturbed viscous circulatory flow around an infinite long cylinder. This
flow is described by 3-D compressible Navier-Stokes equations. By introducing
some suitably weighted energy spaces and establishing a priori estimates, we
show that the 3-D cylindrical symmetric circulatory flow is globally stable in
time when the corresponding initial states are perturbed suitably small.
