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arXiv · 1805.08413

Stochastic nonlinear Schr\"odinger equation with almost space-time white noise

Justin Forlano·Tadahiro Oh·Yuzhao Wang
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Abstract

We study the stochastic cubic nonlinear Schr\"odinger equation (SNLS) with an additive noise on the one-dimensional torus. In particular, we prove local well-posedness of the (renormalized) SNLS when the noise is almost space-time white noise. We also discuss a notion of criticality in this stochastic context, comparing the situation with the stochastic cubic heat equation (also known as the stochastic quantization equation).

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Justin Forlano, Tadahiro Oh, Yuzhao Wang. 2018-05-22. Stochastic nonlinear Schr\"odinger equation with almost space-time white noise. https://arxiv.org/abs/1805.08413

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