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arXiv · 2407.15108

Global well-posedness of the energy-critical stochastic nonlinear Schr\"odinger equation on the three-dimensional torus

Guopeng Li·Mamoru Okamoto·Liying Tao
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Abstract

We study the Cauchy problem of the defocusing energy-critical stochastic nonlinear Schr\"odinger 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 Schr\"odinger 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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Guopeng Li, Mamoru Okamoto, Liying Tao. 2024-07-21. Global well-posedness of the energy-critical stochastic nonlinear Schr\"odinger equation on the three-dimensional torus. https://arxiv.org/abs/2407.15108

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