# On a model of axisymmetric flows in a free boundary domain

## TL;DR

This paper models axisymmetric free boundary vortex flows, identifying vortex boundaries via variational methods and analyzing vortex dynamics through continuity equations, providing a mathematical framework for such fluid phenomena.

## Contribution

It introduces a variational approach to determine vortex boundaries and reduces vortex dynamics to solvable continuity equations, advancing theoretical understanding of axisymmetric flows.

## Key findings

- Vortex boundary characterized by a variational problem.
- Constructed solutions for the continuity equations governing vortex dynamics.
- Provides a mathematical foundation for analyzing free boundary axisymmetric flows.

## Abstract

We consider a model of axisymmetric flows for a free boundary vortex embedded in a statically stable fluid at rest. We identify the boundary of the vortex by solving a variational problem. Then, we reduce the analysis of the dynamics of the vortex to the study of a class of continuity equations for which we construct a solution.