About the wave equation outside two strictly convex obstacles

TL;DR

This paper establishes global Strichartz estimates for the wave equation outside two convex obstacles and explores initial steps toward large data scattering in this geometric setting.

Contribution

It extends Strichartz estimates to the wave equation in a new geometric context and initiates the study of scattering for nonlinear waves near convex obstacles.

Findings

Proved global Strichartz estimates without loss for the wave equation outside two convex obstacles.

Initiated the analysis of large data scattering in this geometric setting.

Proved scattering for non trapping obstacles close to the convex case.

Abstract

We prove global Strichartz estimates without loss for the wave equation outside two strictly convex obstacles, following the roadmap introduced in [Lafontaine, 2017] for the Schr\"odinger equation. Moreover, we show a first step toward the large data scattering for the critical non linear equation associated to this geometrical setting, and prove the scattering for a class of non trapping obstacles close to the two convex framework.