A hyperbolic system and the cost of null controllability for the Stokes system

TL;DR

This paper investigates the cost of null controllability for the Stokes system, demonstrating it grows exponentially as time approaches zero, similar to the heat equation, by linking it to a hyperbolic system with resistance.

Contribution

It establishes the order of the control cost for the Stokes system as T approaches zero and connects it to the controllability of a related hyperbolic system with resistance.

Findings

Cost of null controllability is of order e^{C/T} as T --> 0

Control cost matches that of the heat equation

Controllability of a hyperbolic system with resistance is analyzed

Abstract

This paper is devoted to study the cost of the null controllability for the Stokes system. Using the control transmutation method we show that the cost of driving the Stokes system to rest at time T is of order e^C/T when T -->0^+,i.e., the same order as for the heat equation. For this to be possible, we are led to study the exact controllability of one hyperbolic system with a resistance term, which will be done under assumptions on the control region.