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

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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},
     volume = {16},
     number = {2},
     year = {2010},
     doi = {10.1051/cocv/2009001},
     mrnumber = {2654198},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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, Tome 16 (2010) no. 2, pp. 356-379. doi: 10.1051/cocv/2009001

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