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We prove almost sure global well-posedness of the energy-critical defocusingquintic 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 mainnew ingredient is a uniform probabilistic energy bound for approximating randomsolutions.

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