Stabilization of 2D Navier-Stokes equations by means of actuators with locally supported vorticity

TL;DR

This paper presents a method for exponentially stabilizing 2D Navier-Stokes equations using finite actuators with localized vorticity support, verified through simulations, with applications to observer design.

Contribution

It introduces an explicit feedback control strategy employing localized vorticity actuators for stabilizing 2D Navier-Stokes equations.

Findings

Successful exponential stabilization demonstrated in simulations.

Control effectiveness with finite, localized actuators.

Applicability to observer design problems confirmed.

Abstract

Exponential stabilization to time-dependent trajectories for the incompressible Navier-Stokes equations is achieved with explicit feedback controls. The fluid is contained in two-dimensional spatial domains and the control force is, at each time instant, a linear combination of a finite number of given actuators. Each actuator has its vorticity supported in a small subdomain. The velocity field is subject to Lions boundary conditions. Simulations are presented showing the stabilizing performance of the proposed feedback. The results also apply to a class of observer design problems.