On the controllability of the Navier-Stokes equation in a rectangle, with a little help of a distributed phantom force

TL;DR

This paper discusses the controllability of the Navier-Stokes equations in a rectangular domain, highlighting a novel approach involving a distributed phantom force to achieve control.

Contribution

It provides an overview and proof sketch of new controllability results for Navier-Stokes equations using a distributed phantom force, expanding understanding of fluid control methods.

Findings

Controllability of Navier-Stokes in a rectangle demonstrated

Introduction of a distributed phantom force as a control tool

Sketch of proof outlining key ideas and techniques

Abstract

This note echoes the talk given by the second author during the Journ\'ees EDP 2018 in Obernai. Its aim is to provide an overview and a sketch of proof of the result obtained by the authors, concerning the controllability of the Navier-Stokes equation. We refer the interested readers to the original paper for the full technical details of the proof, which will be omitted here, to focus on the main underlying ideas.