Universality of global dynamics for the cubic wave equation

TL;DR

This paper investigates the universal behavior of solutions to the spherically symmetric focusing cubic wave equation in three dimensions, providing numerical and analytical evidence for a universal attractor that includes both global and blowup solutions.

Contribution

It introduces the concept of a universal attractor for the cubic wave equation and describes the critical behavior at the blowup threshold with explicit detail.

Findings

Existence of a universal attractor for the equation

Characterization of critical blowup behavior

Numerical and analytical support for the attractor

Abstract

We consider the initial value problem for the spherically symmetric, focusing cubic wave equation in three spatial dimensions. We give numerical and analytical evidence for the existence of a universal attractor which encompasses both global and blowup solutions. As a byproduct we get an explicit description of the critical behavior at the threshold of blowup.