On the bilinear control of the Gross-Pitaevskii equation

Thomas Chambrion (1, 2) , Laurent Thomann (1)

1 IECL - Institut Élie Cartan de Lorraine
2 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization

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

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, inPress. ⟨hal-01901819v1⟩