On the bilinear control of the Gross-Pitaevskii equation
Abstract
In this paper we study the bilinear-control problem for the linear and non-linear Schr\"odinger 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.
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