Global controllability and stabilization for the nonlinear Schrödinger equation on an interval
ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 2, pp. 356-379.

We prove global internal controllability in large time for the nonlinear Schrödinger equation on a bounded interval with periodic, Dirichlet or Neumann conditions. Our strategy combines stabilization and local controllability near 0. We use Bourgain spaces to prove this result on L2. We also get a regularity result about the control if the data are assumed smoother.

DOI: 10.1051/cocv/2009001
Classification: 93B05,  93D15,  35Q55,  35A21
Keywords: controllability, stabilization, nonlinear Schrödinger equation, Bourgain spaces
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     author = {Laurent, Camille},
     title = {Global controllability and stabilization for the nonlinear {Schr\"odinger} equation on an interval},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {356--379},
     publisher = {EDP-Sciences},
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     year = {2010},
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     mrnumber = {2654198},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/cocv/2009001/}
}
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Laurent, Camille. Global controllability and stabilization for the nonlinear Schrödinger equation on an interval. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 2, pp. 356-379. doi : 10.1051/cocv/2009001. http://archive.numdam.org/articles/10.1051/cocv/2009001/

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