On the almost sure global well-posedness of energy sub-critical nonlinear wave equations on R3

We consider energy sub-critical defocusing nonlinear wave equations on R-3 and establish the existence of unique global solutions almost surely with respect to a unit-scale randomization of the initial data on Euclidean space. In particular, we provide examples of initial data at super-critical regularities which lead to unique global solutions. The proof is based on probabilistic growth estimates for a new modified energy functional. This work improves upon the authors' previous results (Comm Partial Differential Equations, 2014) by significantly lowering the regularity threshold and strengthening the notion of uniqueness.