Exact controllability of the vortex system by means of a single vortex

TL;DR

This paper demonstrates that a single vortex can control the entire vortex system's positions in finite time, providing a new method for manipulating fluid flow models based on the Euler equations.

Contribution

It introduces a novel control approach for the vortex system using one vortex, establishing exact controllability in a simplified fluid dynamics model.

Findings

Single vortex control can steer all vortices to desired positions

Controllability holds for arbitrary time durations

The method applies to the simplified Euler equation model

Abstract

In this paper, we investigate the controllability of the point vortex system by means of a single vortex. The point vortex system is a well-known simplied model for the incompressible Euler equation, where the vorticity is concentrated in a nite number of Dirac masses. We use one of the vortices as a control, and prove that by suitably choosing its trajectory, we can drive all other vortices to a given prescribed position in arbitrary time.