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

2024/07/21 by Guopeng Li, Mamoru Okamoto, Li, Guopeng +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2407.15108

openalex publication_date 2024/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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