Communications in Mathematical Physics

, Volume 290, Issue 1, pp 371–387 | Cite as

Growth of Sobolev Norms and Controllability of the Schrödinger Equation

  • Vahagn Nersesyan


In this paper we obtain a stabilization result for both linear and nonlinear Schrödinger equations under generic assumptions on the potential. Then we consider the Schrödinger equations 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 the system is almost surely non-bounded in Sobolev spaces.


Function Versus Sobolev Norm Random Potential Unique Continuation Approximate Controllability 
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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesUniversité de Paris-Sud XIOrsay CedexFrance

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