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

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

来源:Arxiv_logoArxiv
英文摘要

We prove global existence and stability of solution to the mass-critical stochastic nonlinear Schr\"odinger 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.

Weijun Xu、Chenjie Fan

10.2140/apde.2021.14.2561

数学物理学

Weijun Xu,Chenjie Fan.Global well-posedness for the defocusing mass-critical stochastic nonlinear Schr\"odinger equation on $\mathbb{R}$ at $L^2$ regularity[EB/OL].(2018-10-18)[2025-08-23].https://arxiv.org/abs/1810.07925.点此复制

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