On the stochastic nonlinear Schr\"odinger equations at critical regularities
Analysis of PDEs
2020-01-28 v2
Abstract
We consider the Cauchy problem for the defocusing stochastic nonlinear Schr\"odinger equations (SNLS) with an additive noise in the mass-critical and energy-critical settings. By adapting the probabilistic perturbation argument employed in the context of the random data Cauchy theory by the first author with B\'enyi and Pocovnicu (2015) to the current stochastic PDE setting, we present a concise argument to establish global well-posedness of the mass-critical and energy-critical SNLS.
Cite
@article{arxiv.1904.06793,
title = {On the stochastic nonlinear Schr\"odinger equations at critical regularities},
author = {Tadahiro Oh and Mamoru Okamoto},
journal= {arXiv preprint arXiv:1904.06793},
year = {2020}
}
Comments
23 pages. Appendix A added. Published in Stoch. Partial Differ. Equ. Anal. Comput