Universality of global dynamics for the cubic wave equation

Agreement between
universal attractor and
numerical solution
during blowup at
every grid point.

First example of
global blowup
for a wave equation.


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 behaviour at the threshold of blowup.