# On the stochastic nonlinear Schr\"odinger equations at critical regularities

## TL;DR

This paper establishes global well-posedness for the defocusing stochastic nonlinear Schrödinger equations at critical regularities using probabilistic perturbation methods, advancing understanding of stochastic PDEs in critical regimes.

## Contribution

It adapts probabilistic perturbation techniques from random data theory to prove global well-posedness for critical stochastic NLS equations.

## Key findings

- Proves global well-posedness at mass-critical regularity.
- Proves global well-posedness at energy-critical regularity.
- Introduces a concise probabilistic perturbation approach.

## 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.