Probabilistic global well-posedness of the viscous nonlinear wave equation with a defocusing quintic nonlinearity

We continue the study of low regularity behavior of the viscous nonlinear wave equation (vNLW) on $mathbb R^2$, initiated by v{C}anic and the first author (2021). In this paper, we focus on the defocusing quintic nonlinearity and, by combining a parabolic smoothing with a probabilistic energy estimate, we prove almost sure global well-posedness of vNLW for initial data in $mathcal H^s (mathbb R^2)$, $s >- frac 15$, under a suitable randomization.