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

Abstract

We consider the Cauchy problem for the defocusing energy-critical stochastic nonlinear wave equations (SNLW) with an additive stochastic forcing on ${\mathbb{R}}^d$ and ${\mathbb{T}}^d$ with $d\ge 3$. 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 ${\mathbb{T}}^d$, we prove global well-posedness with the stochastic forcing below the energy space.

arXiv comment26 pages

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Cited by in corpus (1)

• Global well-posedness of the energy-critical stochastic Hartree nonlinear wave equation