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arXiv · 0905.2438

Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications

Vahagn Nersesyan
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Abstract

We prove that the Schrödinger equation is approximately controllable in Sobolev spaces $H^s$, $s>0$ generically with respect to the potential. We give two applications of this result. First, in the case of one space dimension, combining our result with a local exact controllability property, we get the global exact controllability of the system in higher Sobolev spaces. Then we prove that the Schrödinger equation with a potential which has a random time-dependent amplitude admits at most one stationary measure on the unit sphere $S$ in $L^2 $.

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Vahagn Nersesyan. 2009-05-14. Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications. https://arxiv.org/abs/0905.2438

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