# On the almost sure global well-posedness of energy sub-critical nonlinear wave equations on $\mathbb{R}^3$

@article{Luhrmann2015OnTA, title={On the almost sure global well-posedness of energy sub-critical nonlinear wave equations on \$\mathbb\{R\}^3\$}, author={Jonas Luhrmann and Dana Mendelson}, journal={arXiv: Analysis of PDEs}, year={2015} }

We consider energy sub-critical defocusing nonlinear wave equations on R 3 and establish the existence of unique global solutions al- most 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 modied en-

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