JournalsaihpcVol. 37, No. 3pp. 605–626

On the bilinear control of the Gross-Pitaevskii equation

  • Thomas Chambrion

    Université Bourgogne Franche-Comté, CNRS, IMB, F-21000 Dijon, France

  • Laurent Thomann

    Université de Lorraine, CNRS, IECL, F-54000 Nancy, France
On the bilinear control of the Gross-Pitaevskii equation cover

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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.

Cite this article

Thomas Chambrion, Laurent Thomann, On the bilinear control of the Gross-Pitaevskii equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 3, pp. 605–626

DOI 10.1016/J.ANIHPC.2020.01.001