On the stochastic nonlinear Schrödinger equations at critical regularities.

Tadahiro Oh, Mamoru Okamoto

Research output: Contribution to journalArticlepeer-review


We consider the Cauchy problem for the defocusing stochastic nonlinear Schrödinger 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 Bényi 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.
Original languageEnglish
Pages (from-to)869–894
Number of pages26
JournalStochastics and Partial Differential Equations: Analysis and Computations
Early online date3 Jan 2020
Publication statusPublished - 31 Dec 2020


  • stochastic nonlinear Schrödinger equation
  • global well-posedness
  • mass-critical
  • energy-critical
  • perturbation theory


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