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

  • Vahagn Nersesyan

    Laboratoire de Mathématiques, Université de Paris-Sud XI, Bâtiment 425, 91405 Orsay Cedex, France

Abstract

We prove that the Schrödinger equation is approximately controllable in Sobolev spaces , , 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 .

Cite this article

Vahagn Nersesyan, Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 3, pp. 901–915

DOI 10.1016/J.ANIHPC.2010.01.004