Null Controllability of the Incompressible Stokes Equations in a 2-D Channel Using Normal Boundary Control

TL;DR

This paper proves that the two-dimensional incompressible Stokes equations in a channel can be driven to rest using boundary control on the normal velocity component, employing an observability inequality and a Muntz-Szasz Theorem.

Contribution

It establishes null controllability of the 2D Stokes system with boundary control acting on the normal component, under a zero-average constraint, using novel analytical techniques.

Findings

Null controllability achieved for the 2D Stokes equations in a channel.

Boundary control on the normal velocity component suffices for control.

Utilization of a Muntz-Szasz Theorem in the controllability proof.

Abstract

In this paper, we consider the Stokes equations in a two-dimen- sional channel with periodic conditions in the direction of the channel. We establish null controllability of this system using a boundary control which acts on the normal component of the velocity only. We show null controllability of the system, subject to a constraint of zero average, by proving an observability inequality with the help of a Muntz-Szasz Theorem.