Approximate controllability of the linearized Boussinesq system in a two dimensional channel

TL;DR

This paper proves that it is possible to approximately control the temperature in a 2D Boussinesq fluid system by acting only on the upper boundary, when the system is linearized around a resting fluid.

Contribution

It establishes approximate controllability for the linearized Boussinesq system with boundary temperature control in a 2D channel, a novel result in fluid control theory.

Findings

Approximate controllability is achieved with boundary temperature control.

Control acts only on the upper boundary, simplifying practical implementation.

The result applies to the linearized Boussinesq system in a 2D channel.

Abstract

In this paper, we prove an approximate controllability result for the linearized Boussinesq system around a fluid at rest, in a two dimensional channel, when the control acts only on the temperature, through the upper boundary.