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.

我们在发散的喷嘴中，在输入径向超音速流的细微扰动和喷嘴出口处的恒定压力下，建立了稳定的完整Euler系统的3-D轴对称跨音速激波解的稳定性。为了研究整个Euler系统的3-D轴对称跨音速激波解决方案，我们将完整Euler系统的流函数公式用于3-D轴对称流。我们解决了针对3-D轴对称流的完整Euler系统的流函数公式中出现的奇点问题。我们基于流函数公式，开发了一种新的方案来确定稳定的全欧拉系统的跨音速激波解的激波位置。