Global Controllability and Stabilization for the Nonlinear Schrödinger Equation on Some Compact Manifolds of Dimension 3

Camille Laurent
2010 SIAM Journal on Mathematical Analysis  
We prove global internal controllability in large time for the nonlinear Schrödinger equation on some compact manifolds of dimension 3. The result is proved under some geometrical assumptions : geometric control and unique continuation. We give some examples where they are fulfilled on T 3 , S 3 and S 2 × S 1 . We prove this by two different methods both inherently interesting. The first one combines stabilization and local controllability near 0. The second one uses successive controls near
more » ... e trajectories. We also get a regularity result about the control if the data are assumed smoother. If the H 1 norm is bounded, it gives a local control in H 1 with a smallness assumption only in L 2 . We use Bourgain spaces.
doi:10.1137/090749086 fatcat:egvylrsotjaq5dro2dnd55jsxi