Obstruction and some approximate controllability results for the burgers equation and related problems

Abstract

The paper studies the approximate controllability for the Burgers equation. Due to the presence of a superlinear term, an obstruction phenomenon arises which implies a lack of approximate controllability in spaces of type L^p or $C$. However, the author is able to prove several controllability results under suitable constraints on the desired state. Finally, a necessary condition for the approximate controllability of the Navier-Stokes system on a rectangle is given.