## Analysis & PDE

• Anal. PDE
• Volume 10, Number 6 (2017), 1285-1315.

### 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 $ℝd$. 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.

#### Article information

Source
Anal. PDE, Volume 10, Number 6 (2017), 1285-1315.

Dates
Revised: 14 March 2017
Accepted: 24 April 2017
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.apde/1510843524

Digital Object Identifier
doi:10.2140/apde.2017.10.1285

Mathematical Reviews number (MathSciNet)
MR3678489

Zentralblatt MATH identifier
1372.35262

#### Citation

Khenissi, Moez; Royer, Julien. Local energy decay and smoothing effect for the damped Schrödinger equation. Anal. PDE 10 (2017), no. 6, 1285--1315. doi:10.2140/apde.2017.10.1285. https://projecteuclid.org/euclid.apde/1510843524

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