On the bilinear control of the Gross-Pitaevskii equation

Thomas Chambrion (1) , Laurent Thomann (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 IECL - Institut Élie Cartan de Lorraine

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.

Mots clés: bilinear control; obstructions; Control theory; non-linear Schrödinger equation

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Thomas Chambrion, Laurent Thomann. On the bilinear control of the Gross-Pitaevskii equation. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2020, 37 (3), pp.605--626. ⟨10.1016/j.anihpc.2020.01.001⟩. ⟨hal-01901819v2⟩