Abstract
We consider the radial focusing energy critical nonlinear wave equation in three spatial dimensions. We establish the stability of the ODE-blowup under random perturbations below the energy space. The argument relies on probabilistic Strichartz estimates in similarity coordinates.
Acknowledgments
I would like to thank my advisor Terence Tao for his guidance and support. I would also like to thank Benjamin Harrop-Griffiths, Joachim Krieger, Redmond McNamara, Dana Mendelson, and Tadahiro Oh for helpful discussions.
Notes
1 Strictly speaking, Bourgain [Citation21] worked with random initial data and Da Prato-Debussche [Citation44] worked with a stochastic forcing term. Thus, our setting may be a bit closer to Bourgain’s work [Citation21], but we still chose the terminology Bourgain-Da Prato-Debussche trick.