On the bilinear control of the Gross-Pitaevskii equation

2018/10/23 by Thomas Chambrion, Laurent Thomann, Chambrion, Thomas +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #math.AP #math.OC

paper · pdf · doi:10.48550/arxiv.1810.09792

Annales de l'Institut Henri Poincar{é} (C) Non Linear Analysis, Elsevier, In press

arxiv created 2020/01/20 · arxiv updated 2020/01/22

Abstract

In this paper we study the bilinear-control problem for the linear and non-linear Schrödinger equation with harmonic potential. By the means of different examples, we show how space-time smoothing effects (Strichartz estimates, Kato smoothing effect) enjoyed by the linear flow, can help to prove obstructions to controllability.

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