The jet problem for three-dimensional axially symmetric full compressible subsonic flows with nonzero vorticity

In this paper, we show that for given Bernoulli function and entropy function at the upstream, if the incoming mass flux is within a suitable range, then there exists a unique outer pressure such that smooth subsonic three-dimensional axially symmetric jet flows for steady full Euler system with nonzero vorticity exist and have certain far fields behavior. A key observation is that we can transform the jet problem for three-dimensional axially symmetric steady full Euler system with nonzero vorticity into a variational problem in terms of the stream function. Moreover, using uniform estimates of the stream function and the iteration method, we exclude the singularity of the jet flows near the symmetry axis.