An elementary proof of global existence for nonlinear wave equations in an exterior domain

TL;DR

This paper provides a simple proof of global existence for nonlinear wave equations satisfying the null condition in exterior domains, avoiding complex scaling operators by employing new weighted pointwise estimates.

Contribution

It introduces an elementary proof technique that bypasses the need for scaling operators, simplifying the analysis of nonlinear wave equations in exterior domains.

Findings

Proves global existence for nonlinear wave equations with null condition

Develops new weighted pointwise estimates for tangential derivatives

Simplifies previous complex proof methods

Abstract

The aim of this article is to present an elementary proof of a global existence result for nonlinear wave equations satifying the null condition in an exterior domain. The novelty of our proof is to avoid completely the scaling operator which would make the argument complicated in the mixed problem, by using a new weighted pointwise estimates of a tangential derivative to the light cone.