Stochastic nonlinear Schrödinger equation with almost space-time white noise
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).
arXiv comment22 pages. To appear in J. Aust. Math. Soc
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