  We establish the stability of 3-D axisymmetric transonic shock solutions of
the steady full Euler system in divergent nozzles under small perturbations of
an incoming radial supersonic flow and a constant pressure at the exit of the
nozzles. To study 3-D axisymmetric transonic shock solutions of the full Euler
system, we use a stream function formulation of the full Euler system for a 3-D
axisymmetric flow. We resolve the singularity issue arising in stream function
formulations of the full Euler system for a 3-D axisymmetric flow. We develop a
new scheme to determine a shock location of a transonic shock solution of the
steady full Euler system based on the stream function formulation.
