Stabilization and control for the nonlinear Schrödinger equation on a compact surface (Q2457746)

The stabilization property and the exact controllability for the nonlinear Schrödinger equation on a two dimensional Riemannian manifold without boundary is investigated. The authors use a pseudo-differential dissipation. The proofs are based on a result of propagation of singularities and on recent dispertion estimates reported in [\textit{N. Burq, P. Gérard} and \textit{N. Tzvetkov}, Am. J. Math. 126, No. 3, 569--605 (2004; Zbl 1067.58027)].