Growth of Sobolev norms and controllability of Schrödinger equation

Details Growth of Sobolev norms and controllability of Schrödinger equation Growth of Sobolev norms and controllability of Schrödinger equation

2008-04-24

arxiv.org/abs/0804.3982v2

Mathematics

Analysis of PDEs

Scientific paper

In this paper we obtain a stabilization result for the Schr\"odinger equation
under generic assumptions on the potential. Then we consider the Schr\"odinger
equation with a potential which has a random time-dependent amplitude. We show
that if the distribution of the amplitude is sufficiently non-degenerate, then
any trajectory of system is almost surely non-bounded in Sobolev spaces.

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