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

Abstract

We prove global existence and stability of solution to the mass-critical stochastic nonlinear Schrödinger equation in $d=1$ at $L^2$ regularity. Our construction starts with the existence of 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.

37 pages. The material presented in this article is a re-orgasination of arXiv:1803.03257 and part of arXiv:1807.04402 of the authors. The other part of arXiv:1807.04402, which has not been covered in the current article, will be re-written as another independent one (forthcoming). Only the current article and the forthcoming one will be submitted for journal publication

References in corpus (2)

• Stochastic integration in UMD Banach spaces
• Scattering for stochastic nonlinear Schrödinger equations