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arXiv · 1904.06793

On the stochastic nonlinear Schr\"odinger equations at critical regularities

Tadahiro Oh·Mamoru Okamoto
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Abstract

We consider the Cauchy problem for the defocusing stochastic nonlinear Schr\"odinger 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 the first author with B\'enyi and Pocovnicu (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.

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Tadahiro Oh, Mamoru Okamoto. 2019-04-15. On the stochastic nonlinear Schr\"odinger equations at critical regularities. https://doi.org/10.1007/s40072-019-00163-5

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