We consider the Cauchy problem for the defocusing stochastic nonlinear Schrödinger 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 Bényi et al. (Trans Am Math Soc Ser B 2:1–50, 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.

中文翻译：

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临界规则下的随机非线性Schrödinger方程

对于质量临界和能量临界设置中具有加性噪声的散焦随机非线性Schrödinger方程（SNLS），我们考虑了柯西问题。通过适应在随机数据上下文中使用的概率摄动论证，Bényi等人提出了柯西理论。（Trans Am Math Soc Ser B 2：1–50，2015年）到目前的随机PDE设置，我们提出了一个简洁的论据来建立质量关键型和能量关键型SNLS的全球适度性。