Decay estimates for variable coefficient wave equations in exterior domains

TL;DR

This paper establishes decay and energy estimates for variable coefficient wave equations in exterior domains, demonstrating localized energy decay in star-shaped domains and global Strichartz estimates in strictly convex domains.

Contribution

It provides new decay estimates for variable coefficient wave equations in exterior domains, extending known results to more general geometries.

Findings

Localized energy decay in star-shaped domains.

Global Strichartz estimates in strictly convex domains.

Extension of decay estimates to variable coefficient wave equations.

Abstract

In this article we consider variable coefficient, time dependent wave equations in exterior domains. We prove localized energy estimates if the domain is star-shaped and global in time Strichartz estimates if the domain is strictly convex.