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

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.

Keywords:

• Blow-up
• energy critical
• nonlinear wave equations
• random initial data

AMS SUBJECT CLASSIFICATIONS MSC 2010:

• 35L05
• 35L15
• 35L71

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 [21] worked with random initial data and Da Prato-Debussche [44] worked with a stochastic forcing term. Thus, our setting may be a bit closer to Bourgain’s work [21], but we still chose the terminology Bourgain-Da Prato-Debussche trick.