The fractional Schrödinger equation on compact manifolds: Global controllability results

Abstract

The goal of this work is to prove global controllability and stabilization properties for the fractional Schrödinger equation on $d$-dimensional compact Riemannian manifolds without boundary $(M,g)$. To prove our main results we use techniques of pseudo-differential calculus on manifolds. More precisely, by using microlocal analysis, we are able to prove propagation of regularity which together with the so-called Geometric Control Condition and Unique Continuation Property help us to prove global control results for the system under consideration. As a main novelty this manuscript presents the relation between the geometric control condition and the controllability for the fractional Schrödinger equation.

27 pages

References in corpus (3)

• Semiclassical measures and the Schroedinger flow on Riemannian manifolds
• Stabilization and control for the biharmonic Schrödinger equation
• Control of three dimensional water waves