Resolvent estimates in strips for obstacle scattering in 2D and local energy decay for the wave equation

TL;DR

This paper establishes polynomial resolvent estimates for obstacle scattering in 2D and applies these results to demonstrate local energy decay for the wave equation, advancing understanding of wave behavior around convex obstacles.

Contribution

It provides new polynomial resolvent estimates in strips below the real axis for convex obstacle scattering in 2D, leading to improved energy decay results.

Findings

Polynomial resolvent estimates in strips below the real axis

O(|λ| log |λ|) bounds for the truncated resolvent on the real line

Application to local energy decay for the wave equation

Abstract

In this note, we are interested in the problem of scattering by J strictly convex obstacles satisfying a no-eclipse condition in dimension 2. We use the result of a previous article of the author to obtain polynomial resolvent estimates in strips below the real axis. We deduce estimates in O(|$\lambda$| log |$\lambda$|) for the truncated resolvent on the real line and give an application to the decay of the local energy for the wave equation.