Almost conservation laws for stochastic nonlinear Schrödinger equations

Kelvin Cheung, Guopeng Li, Tadahiro Oh

Research output: Contribution to journalArticlepeer-review


In this paper, we present a globalization argument for stochastic nonlinear dispersive PDEs with additive noises by adapting the I-method (= the method of almost conservation laws) to the stochastic setting. As a model example, we consider the defocusing stochastic cubic nonlinear Schrödinger equation (SNLS) on R3 with additive stochastic forcing, white in time and correlated in space, such that the noise lies below the energy space. By combining the I-method with Ito's lemma and a stopping time argument, we construct global-in-time dynamics for SNLS below the energy space.
Original languageEnglish
Number of pages30
JournalJournal of Evolution Equations
Early online date20 Jan 2021
Publication statusE-pub ahead of print - 20 Jan 2021


  • stochastic nonlinear Schrödinger equation
  • global well-posedness
  • I-method
  • almost conservation law


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