On the bilinear control of the Gross-Pitaevskii equation
Chambrion, Thomas1 ; Thomann, Laurent2
1 Université Bourgogne Franche-Comté, CNRS, IMB, F-21000 Dijon, France
2 Université de Lorraine, CNRS, IECL, F-54000 Nancy, France
Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 3, pp. 605-626.
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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.

DOI : 10.1016/j.anihpc.2020.01.001
Classification : 35Q93, 35L05
Mots-clés : Control theory, Bilinear control, Obstructions, Non-linear Schrödinger equation
Chambrion, Thomas 1 ; Thomann, Laurent 2

1 Université Bourgogne Franche-Comté, CNRS, IMB, F-21000 Dijon, France
2 Université de Lorraine, CNRS, IECL, F-54000 Nancy, France 
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Chambrion, Thomas; Thomann, Laurent. On the bilinear control of the Gross-Pitaevskii equation. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 3, pp. 605-626. doi : 10.1016/j.anihpc.2020.01.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2020.01.001/

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