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

@article{Laurent2010GlobalCA, title={Global Controllability and Stabilization for the Nonlinear Schr{\"o}dinger Equation on Some Compact Manifolds of Dimension 3}, author={Camille Laurent}, journal={SIAM J. Math. Anal.}, year={2010}, volume={42}, pages={785-832} }

We prove global internal controllability in large time for the nonlinear Schr\"odinger 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 $\Tot$, $S^3$ and $S^2\times S^1$. 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…

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