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

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles