Stable blowup for the focusing energy critical nonlinear wave equation under random perturbations

Bjoern Bringmann

Published 2020-02-18Version 1

We consider the radial focusing energy critical nonlinear wave equation in three spatial dimensions. Our main result proves the stability of the ODE-blowup under random perturbations below the energy space. To the best of our knowledge, this is the first study of blowup in dispersive equations with random initial data. The argument relies on probabilistic Strichartz estimates in similarity coordinates for the linearized evolution around the ODE-blowup.