The stochastic nonlinear Schrödinger equation in H1

A. De Bouard; A. Debussche

doi:10.1081/SAP-120017534

The stochastic nonlinear Schrödinger equation in H¹

A. De Bouard
, A. Debussche

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

Abstract

We investigate the local and global existence of solutions in the energy space H¹(ℝⁿ) for stochastic nonlinear Schrödinger equations with either additive or multiplicative noise. The noise is assumed to be white in time and correlated in the space variables.

Original language	English
Pages (from-to)	97-126
Number of pages	30
Journal	Stochastic Analysis and Applications
Volume	21
Issue number	1
DOIs	https://doi.org/10.1081/SAP-120017534
Publication status	Published - 1 Jan 2003

Keywords

Nonlinear Schrödinger equations
Stochastic partial differential equations
White noise

Access to Document

10.1081/SAP-120017534

Cite this

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title = "The stochastic nonlinear Schr{\"o}dinger equation in H1",

abstract = "We investigate the local and global existence of solutions in the energy space H1(ℝn) for stochastic nonlinear Schr{\"o}dinger equations with either additive or multiplicative noise. The noise is assumed to be white in time and correlated in the space variables.",

keywords = "Nonlinear Schr{\"o}dinger equations, Stochastic partial differential equations, White noise",

author = "\{De Bouard\}, A. and A. Debussche",

year = "2003",

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AU - Debussche, A.

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N2 - We investigate the local and global existence of solutions in the energy space H1(ℝn) for stochastic nonlinear Schrödinger equations with either additive or multiplicative noise. The noise is assumed to be white in time and correlated in the space variables.

AB - We investigate the local and global existence of solutions in the energy space H1(ℝn) for stochastic nonlinear Schrödinger equations with either additive or multiplicative noise. The noise is assumed to be white in time and correlated in the space variables.

KW - Nonlinear Schrödinger equations

KW - Stochastic partial differential equations

KW - White noise

U2 - 10.1081/SAP-120017534

DO - 10.1081/SAP-120017534

M3 - Article

AN - SCOPUS:0037282052

SN - 0736-2994

VL - 21

SP - 97

EP - 126

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

IS - 1