Blow-up for the stochastic nonlinear Schrödinger equation with multiplicative noise

Anne De Bouard; Arnaud Debussche

doi:10.1214/009117904000000964

Blow-up for the stochastic nonlinear Schrödinger equation with multiplicative noise

Anne De Bouard
, Arnaud Debussche

ENS Paris-Saclay

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

Abstract

We study the influence of a multiplicative Gaussian noise, white in time and correlated in space, on the blow-up phenomenon in the supercritical nonlinear Schrödinger equation. We prove that any sufficiently regular and localized deterministic initial data gives rise to a solution which blows up in arbitrarily small time with a positive probability.

Original language	English
Pages (from-to)	1078-1110
Number of pages	33
Journal	Annals of Probability
Volume	33
Issue number	3
DOIs	https://doi.org/10.1214/009117904000000964
Publication status	Published - 1 May 2005

Keywords

Blow-up
Nonlinear Schrödinger equations
Stochastic partial differential equations
Support theorem
Variance identity
White noise

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10.1214/009117904000000964

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title = "Blow-up for the stochastic nonlinear Schr{\"o}dinger equation with multiplicative noise",

abstract = "We study the influence of a multiplicative Gaussian noise, white in time and correlated in space, on the blow-up phenomenon in the supercritical nonlinear Schr{\"o}dinger equation. We prove that any sufficiently regular and localized deterministic initial data gives rise to a solution which blows up in arbitrarily small time with a positive probability.",

keywords = "Blow-up, Nonlinear Schr{\"o}dinger equations, Stochastic partial differential equations, Support theorem, Variance identity, White noise",

author = "\{De Bouard\}, Anne and Arnaud Debussche",

year = "2005",

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AU - De Bouard, Anne

AU - Debussche, Arnaud

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N2 - We study the influence of a multiplicative Gaussian noise, white in time and correlated in space, on the blow-up phenomenon in the supercritical nonlinear Schrödinger equation. We prove that any sufficiently regular and localized deterministic initial data gives rise to a solution which blows up in arbitrarily small time with a positive probability.

AB - We study the influence of a multiplicative Gaussian noise, white in time and correlated in space, on the blow-up phenomenon in the supercritical nonlinear Schrödinger equation. We prove that any sufficiently regular and localized deterministic initial data gives rise to a solution which blows up in arbitrarily small time with a positive probability.

KW - Blow-up

KW - Nonlinear Schrödinger equations

KW - Stochastic partial differential equations

KW - Support theorem

KW - Variance identity

KW - White noise

UR - https://www.scopus.com/pages/publications/18844383396

U2 - 10.1214/009117904000000964

DO - 10.1214/009117904000000964

M3 - Article

AN - SCOPUS:18844383396

SN - 0091-1798

VL - 33

SP - 1078

EP - 1110

JO - Annals of Probability

JF - Annals of Probability

IS - 3

ER -

Blow-up for the stochastic nonlinear Schrödinger equation with multiplicative noise

Abstract

Keywords

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