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

TL;DR

This paper proves the existence and uniqueness of smooth, subsonic, axially symmetric jet flows with nonzero vorticity in three-dimensional steady Euler systems, transforming the problem into a variational framework and controlling singularities near the axis.

Contribution

It introduces a novel variational approach to analyze three-dimensional axially symmetric jet flows with vorticity, establishing existence and uniqueness results.

Findings

Existence of unique smooth subsonic jet solutions under certain conditions.

Transformation of the jet problem into a variational problem using stream functions.

Control of flow singularities near the symmetry axis.

Abstract

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.