Unconditional wave decay in dimension two

TL;DR

This paper extends wave decay results in two dimensions to more general scatterers by removing spectral regularity constraints, enabling analysis of complex obstacles with variable boundary conditions.

Contribution

It introduces a new approach using low-frequency expansions to generalize wave decay results to arbitrary smooth obstacles with variable boundary conditions in two dimensions.

Findings

Extended decay rate to general compactly supported scatterers in 2D.

Removed spectral regularity constraints at zero frequency.

Included complex obstacles with variable boundary conditions.

Abstract

We extend Burq's logarithmic decay rate [Bur98] to general compactly supported scatterers in dimension two. The main novelty is using recent results on low-frequency expansions to remove the requirement that the spectrum be regular at zero. This allows us to include, among other examples, arbitrary smooth obstacles with variable boundary conditions.