Global well-posedness of the energy-critical stochastic nonlinear Schrödinger equation on the three-dimensional torus

Abstract

We study the Cauchy problem of the defocusing energy-critical stochastic nonlinear Schrödinger equation (SNLS) on the three dimensional torus, forced by an additive noise. We adapt the atomic spaces framework in the context of the energy-critical nonlinear Schrödinger equation, and employ probabilistic perturbation arguments in the context of stochastic PDEs, establishing the global well-posedness of the defocusing energy-critical quintic SNLS in the energy space. It is the first global well-posedness result for the periodic SNLS in a critical space.

20 pages. Minor typos corrected and authors' affiliations updated