Stochastic nonlinear Schrödinger equation with almost space-time white noise

2018/05/22 by Forlano, Justin, Oh, Tadahiro, Wang, Yuzhao
#35Q55 #60H30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1805.08413

Abstract

We study the stochastic cubic nonlinear Schrödinger 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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