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.

中文翻译：

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Gross-Pitaevskii方程的双线性控制

在本文中，我们研究具有谐和势的线性和非线性Schrödinger方程的双线性控制问题。通过不同的例子，我们展示了线性流如何享受时空平滑效果（Strichartz估计，Kato平滑效果），可以帮助证明对可控性的阻碍。