Vol. 10, No. 6, 2017

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ISSN: 1948-206X (e-only)
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Local energy decay and smoothing effect for the damped Schrödinger equation

Moez Khenissi and Julien Royer

Vol. 10 (2017), No. 6, 1285–1315
Abstract

We prove the local energy decay and the global smoothing effect for the damped Schrödinger equation on 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.

Keywords
local energy decay, smoothing effect, damped Schrödinger equation, resolvent estimates
Mathematical Subject Classification 2010
Primary: 35B40, 35Q41, 35B65, 47A55, 47B44
Milestones
Received: 3 June 2015
Revised: 14 March 2017
Accepted: 24 April 2017
Published: 14 July 2017
Authors
Moez Khenissi
LAMMDA
École Supérieure des Sciences et de Technologie de Hammam Sousse
Université de Sousse
Rue Lamine El Abbessi
4011 Hammam Sousse
Tunisia
Julien Royer
Institut de Mathématiques de Toulouse
118, route de Narbonne
31062 Toulouse Cédex 9
France