Local energy decay and smoothing effect for the damped Schrödinger equation

Moez Khenissi (1) , Julien Royer (2)

1 Ecole supérieur de Sciences et Technique de Hammam Sousse
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We prove the local energy decay and the 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 which we consider.

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Moez Khenissi, Julien Royer. Local energy decay and smoothing effect for the damped Schrödinger equation. Analysis & PDE, 2017, 10 (6). ⟨hal-01155498⟩