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On the stochastic nonlinear Schrödinger equations at critical regularities.

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Original languageEnglish
Number of pages26
JournalStochastic Partial Differential Equations: Analysis and Computations
Early online date3 Jan 2020
DOIs
Publication statusE-pub ahead of print - 3 Jan 2020

Abstract

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.

    Research areas

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

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