Dispersion estimates for the wave equation outside of a cylinder]{Dispersive estimates for the wave equation outside a cylinder in $\mathbb{R}^3$

TL;DR

This paper derives sharp dispersion and Strichartz estimates for the wave equation outside a cylinder in three-dimensional space, matching the known estimates in free space, by constructing a global parametrix.

Contribution

It introduces a global parametrix for the wave equation outside a cylinder, enabling sharp dispersion estimates across all frequencies, including low and high.

Findings

Established sharp dispersion estimates matching free space in R^3

Derived Strichartz estimates for the exterior wave problem

Constructed a global in time parametrix for the wave equation

Abstract

We consider the wave equation with Dirichlet boundary conditions in the exterior of a cylinder in R 3 and we construct a global in time parametrix to derive sharp dispersion estimates for all frequencies (low and high) and, as a corollary, Strichartz estimates, all matching the R 3 case.