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

We prove global existence and stability of the solution to the mass-critical stochastic nonlinear Schrödinger equation in d = 1 with LωLx2 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.

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NLS, stochastic, mass critical
Mathematical Subject Classification 2010
Primary: 35Q55, 60H15
Received: 27 October 2019
Revised: 21 May 2020
Accepted: 31 July 2020
Published: 19 December 2021
Chenjie Fan
Department of Mathematics
University of Chicago
Chicago, IL
United States
Weijun Xu
Beijing International Center for Mathematical Research
Peking University