Global well-posedness of the energy-critical stochastic nonlinear wave equations

We consider the Cauchy problem for the defocusing energy-critical stochastic nonlinear wave equations (SNLW) with an additive stochastic forcing on Rd and Td with d≥3. By adapting the probabilistic perturbation argument employed in the context of the random data Cauchy theory by Bényi-Oh-Pocovnicu (2015) and Pocovnicu (2017) and in the context of stochastic PDEs by Oh-Okamoto (2020), we prove global well-posedness of the defocusing energy-critical SNLW. In particular, on Td, we prove global well-posedness with the stochastic forcing below the energy space.