Local energy decay for several evolution equations on asymptotically euclidean manifolds

Abstract

Let P be a long range metric perturbation of the Euclidean Laplacian on R^d, d>1. We prove local energy decay for the solutions of the wave, Klein-Gordon and Schroedinger equations associated to P. The problem is decomposed in a low and high frequency analysis. For the high energy part, we assume a non trapping condition. For low (resp. high) frequencies we obtain a general result about the local energy decay for the group exp(itf(P)) where f has a suitable development at zero (resp. infinity).