Strichartz estimates on exterior polygonal domains

TL;DR

This paper establishes new local and global Strichartz and smoothing estimates for wave equations outside polygonal obstacles, advancing understanding of wave behavior in complex geometric settings.

Contribution

It introduces novel local smoothing estimates and extends Strichartz estimates to exterior polygonal domains with various boundary conditions.

Findings

Proved local-in-time Strichartz estimates without loss

Established global-in-time Strichartz estimates for polygonal obstacles

Derived global local smoothing estimates in wedge domains

Abstract

Using a new local smoothing estimate of the first and third authors, we prove local-in-time Strichartz and smoothing estimates without a loss exterior to a large class of polygonal obstacles with arbitrary boundary conditions and global-in-time Strichartz estimates without a loss exterior to a large class of polygonal obstacles with Dirichlet boundary conditions. In addition, we prove a global-in-time local smoothing estimate in exterior wedge domains with Dirichlet boundary conditions and discuss some nonlinear applications.