Global controllability and stabilization for the nonlinear Schrodinger equation on an interval

TL;DR

This paper establishes global controllability and stabilization results for the nonlinear Schrödinger equation on an interval, using Bourgain spaces and combining stabilization with local controllability techniques.

Contribution

It introduces a novel approach combining stabilization and local controllability near zero for the nonlinear Schrödinger equation on bounded domains.

Findings

Proves global internal controllability in large time for the nonlinear Schrödinger equation.

Uses Bourgain spaces to establish controllability on L2.

Provides regularity results for the control with smoother data.

Abstract

We prove global internal controllability in large time for the nonlinear Schrodinger equation on a bounded interval with periodic, Dirichlet or Neumann conditions. Our strategy combines stabilization and local controllability near 0. We use Bourgain spaces to prove this result on L2. We also get a regularity result about the control if the data are assumed smoother.