A Hyperbolic system and the cost of the controllability for the Stokes system

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^{CIT} when T⟶0+ , i.e., the same order of controllability as for the heat equation. For this to be possible, we prove a new exact controllability result for a hyperbolic system with a resistance term, which will be done under assumptions on the control region.