Approximate controllability for 2D Euler equations

TL;DR

This paper investigates the approximate controllability of 2D Euler equations using a finite set of actuators, introducing a relaxed saturating set condition that guarantees controllability on general bounded domains.

Contribution

It introduces a relaxed notion of saturating set for actuators, broadening the conditions under which approximate controllability of 2D Euler equations can be achieved.

Findings

Approximate controllability holds with a saturating set of actuators.

The relaxed saturating set condition is sufficient for controllability.

The results apply to general bounded 2D domains with smooth boundaries.

Abstract

Approximate controllability of the Euler equations is investigated by means of a finite set of actuators. It is proven that approximate controllability holds if we can find a saturating subset of actuators. The notion of saturating set is relaxed when compared to previous literature, still being a sufficient condition for approximate controllability. The result holds for general bounded two-dimensional spatial domains with smooth boundary. An example of a saturating set is given in the case the spatial domain is the unit disk.