Structural stability of transonic shock flows with external force in a divergent 3-D axisymmetric perturbed nozzle

Abstract

This paper concerns with the structural stability of the transonic shock for steady Euler flows with external force in a divergent 3-D axisymmetric perturbed nozzle. We first establish the existence and uniqueness of spherical symmetric transonic shock solution to steady isentropic Euler system with external force by prescribing suitable exit pressure at the exit of a straight divergent nozzle when the incoming flow at the entrance is spherical symmetric supersonic flow. Then we investigate the stability of this spherical symmetric transonic shock solution to the 3-D axisymmetric steady isentropic Euler system with external force when the incoming supersonic flow and the nozzle boundary and the exit pressure and the external force are suitable perturbed. One of new ideas in the analysis is to use the deformation-curl decomposition provided in [21] to deal with the transonic shock problem.