  We address the structural stability of 3-D axisymmetric subsonic flows with
nonzero swirl for the steady compressible Euler-Poisson system in a cylinder
supplemented with non small boundary data. A special Helmholtz decomposition of
the velocity field is introduced for 3-D axisymmetric flow with a nonzero
swirl(=angular momentum density) component.
  With the newly introduced decomposition, a quasilinear elliptic system of
second order is derived from the elliptic modes in Euler-Poisson system for
subsonic flows. Due to the nonzero swirl, the main difficulties lie in the
solvability of a singular elliptic equation which concerns the angular
component of the vorticity in its cylindrical representation, and in analysis
of streamlines near the axis $r=0$.
