#### Vol. 14, No. 8, 2021

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Global well-posedness for the defocussing mass-critical stochastic nonlinear Schrödinger equation on $\mathbb{R}$ at $L^{2}$ regularity

### Chenjie Fan and Weijun Xu

Vol. 14 (2021), No. 8, 2561–2594
##### Abstract

We prove global existence and stability of the solution to the mass-critical stochastic nonlinear Schrödinger equation in $d=1$ with ${L}_{\omega }^{\infty }{L}_{x}^{2}$ initial data. Our construction starts with the existence of a solution to the truncated subcritical problem. With the presence of truncation, we construct the solution to the critical equation as the limit of subcritical solutions. We then obtain uniform bounds on the solutions to the truncated critical problems that allow us to remove truncation in the limit.

##### Keywords
NLS, stochastic, mass critical
##### Mathematical Subject Classification 2010
Primary: 35Q55, 60H15
##### Milestones
Revised: 21 May 2020
Accepted: 31 July 2020
Published: 19 December 2021
##### Authors
 Chenjie Fan Department of Mathematics University of Chicago Chicago, IL United States Weijun Xu Beijing International Center for Mathematical Research Peking University Beijing China