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On the stochastic nonlinear Schrödinger equations at critical regularities
Stochastics and Partial Differential Equations: Analysis and Computations ( IF 1.4 ) Pub Date : 2020-01-03 , DOI: 10.1007/s40072-019-00163-5
Tadahiro Oh , Mamoru Okamoto

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:

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。

更新日期:2020-01-03
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