A Positivity Criterion for the Wave Equation and Global Existence of Large Solutions

Abstract

In dimensions one to three, the fundamental solution to the free wave equation is positive. Therefore, there exists a simple positivity criterion for solutions. We use this to obtain large global solutions to two well-studied energy-supercritical semilinear wave equations, as well as some new results in the subcritical and critical cases.

arXiv comment35 pages This version was accepted for publication by IMRN in May 2023