Stochastic nonlinear Schrödinger equation with almost space-time white noise

Justin Forlano; Tadahiro Oh; Yuzhao Wang

doi:10.1017/S1446788719000156

Stochastic nonlinear Schrödinger equation with almost space-time white noise

Justin Forlano, Tadahiro Oh^*, Yuzhao Wang

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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).

Original language	English
Pages (from-to)	44-67
Number of pages	24
Journal	Journal of the Australian Mathematical Society
Volume	109
Issue number	1
DOIs	https://doi.org/10.1017/S1446788719000156
Publication status	Published - 1 Aug 2020

Keywords

Fourier Lebesgue spaces
Stochastic nonlinear Schrodinger equation
Well-posedness
White noise

ASJC Scopus subject areas

Mathematics(all)

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10.1017/S1446788719000156

Cite this

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title = "Stochastic nonlinear Schr{\"o}dinger equation with almost space-time white noise",

abstract = "We study the stochastic cubic nonlinear Schr{\"o}dinger 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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AU - Oh, Tadahiro

AU - Wang, Yuzhao

PY - 2020/8/1

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N2 - 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).

AB - 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).

KW - Fourier Lebesgue spaces

KW - Stochastic nonlinear Schrodinger equation

KW - Well-posedness

KW - White noise

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DO - 10.1017/S1446788719000156

M3 - Article

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JF - Journal of the Australian Mathematical Society

IS - 1

ER -

Stochastic nonlinear Schrödinger equation with almost space-time white noise

Abstract

Keywords

ASJC Scopus subject areas

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