Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on $\mathbb{R}^3$

Abstract

We prove almost sure global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on $\mathbb{R}^3$ with random initial data in $ H^s(\mathbb{R}^3) \times H^{s-1}(\mathbb{R}^3)$ for $s > \frac 12$. The main new ingredient is a uniform probabilistic energy bound for approximating random solutions.

26 pages. Expanded the introduction. To appear in J. Math. Pures Appl