Contact discontinuities for axisymmetric subsonic flows in three-dimensional infinitely long cylinders

TL;DR

This paper proves the existence of contact discontinuities in axisymmetric subsonic Euler flows within infinite cylinders, using a novel iterative approach to solve a complex free boundary problem.

Contribution

It introduces a new method to establish contact discontinuities for subsonic flows with vorticity in 3D cylinders, employing a Helmholtz decomposition and iterative scheme.

Findings

Existence of contact discontinuities in the specified flow conditions.

Development of a new iterative method for free boundary problems.

Reformulation of the problem using Helmholtz decomposition.

Abstract

We prove the existence of contact discontinuities for axisymmetric subsonic Euler flows with non-zero vorticity and non-zero angular momentum density in three-dimensional infinitely long cylinders. The problem is formulated as a two-phase free boundary problem in a cylinder of infinite length. We first solve the cut-off domain problem and take the limit. The cut-off domain problem is reformulated by using a Helmholtz decomposition method and solved via an iteration method. A sophisticated iteration scheme is devised to solve the two-phase free boundary problem.