Classification of radial solutions of the focusing, energy-critical wave equation

TL;DR

This paper analyzes the long-term behavior of radial solutions to the energy-critical focusing wave equation in three dimensions, including solutions that exist globally and those that blow up in finite time.

Contribution

It provides a detailed description of the asymptotic behavior of solutions, advancing understanding of the dynamics of the energy-critical wave equation.

Findings

Characterization of global solutions' asymptotics

Description of finite-time blow-up behavior

Insights into solution stability and singularity formation

Abstract

In this paper, we describe the asymptotic behaviour of globally defined solutions and of bounded solutions blowing up in finite time of the radial energy-critical focusing non-linear wave equation in three space dimension.