Global Strichartz Estimates for Solutions to the Wave Equation Exterior to a Convex Obstacle

TL;DR

This paper extends local Strichartz estimates for wave equations outside convex obstacles to global estimates in space and time, building upon prior work in odd dimensions.

Contribution

It provides the first known extension of local to global Strichartz estimates for wave equations exterior to convex obstacles in all spatial dimensions.

Findings

Global Strichartz estimates are established for wave solutions outside convex obstacles.

The results generalize previous odd-dimensional cases to all dimensions.

The work advances understanding of wave behavior in exterior domains.

Abstract

In this paper, we show that certain local Strichartz estimates for solutions of the wave equation exterior to a convex obstacle can be extended to estimates that are global in both space and time. This extends the work that was done previously by H. Smith and C. Sogge in odd spatial dimensions.