Local energy decay and smoothing effect for the damped Schrödinger equation

Abstract

We prove the local energy decay and the global smoothing effect for the damped Schrödinger equation on ${ℝ}^d$. The self-adjoint part is a Laplacian associated to a long-range perturbation of the flat metric. The proofs are based on uniform resolvent estimates obtained by the dissipative Mourre method. All the results depend on the strength of the dissipation that we consider.