The authors prove existence, uniqueness, and structural stability of transonic shocks for the 3D axisymmetric Euler system with swirl under small perturbations of the incoming supersonic flow, nozzle boundary, and exit pressure.
Chen, Stability of transonic shock fronts in two-dimensional Euler systems, Trans
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Structural stability of the transonic shock problem in a divergent three dimensional axisymmetric perturbed nozzle
The authors prove existence, uniqueness, and structural stability of transonic shocks for the 3D axisymmetric Euler system with swirl under small perturbations of the incoming supersonic flow, nozzle boundary, and exit pressure.