Improved local energy decay for the wave equation on asymptotically Euclidean odd dimensional manifolds in the short range case

TL;DR

This paper demonstrates enhanced local energy decay rates for the wave equation on asymptotically Euclidean odd-dimensional manifolds, with decay depending on metric convergence, and provides resolvent estimates in weighted spaces.

Contribution

It introduces improved decay estimates for the wave equation on asymptotically Euclidean manifolds in odd dimensions, extending previous results in the short range case.

Findings

Enhanced local energy decay rates established

Decay rate depends on metric convergence to Euclidean metric

Provides resolvent estimates between weighted spaces

Abstract

We show improved local energy decay for the wave equation on asymptotically Euclidean manifolds in odd dimensions in the short range case. The precise decay rate depends on the decay of the metric towards the Euclidean metric. We also give estimates of powers of the resolvent of the wave propagator between weighted spaces.