Stochastic nonlinear Schr\"odinger equation with almost space-time white noise
Analysis of PDEs
2019-02-19 v2 Probability
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).
Keywords
Cite
@article{arxiv.1805.08413,
title = {Stochastic nonlinear Schr\"odinger equation with almost space-time white noise},
author = {Justin Forlano and Tadahiro Oh and Yuzhao Wang},
journal= {arXiv preprint arXiv:1805.08413},
year = {2019}
}
Comments
22 pages. To appear in J. Aust. Math. Soc