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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Pages (de - à)	1078-1110
Nombre de pages	33
journal	Annals of Probability
Volume	33
Numéro de publication	3
Les DOIs	https://doi.org/10.1214/009117904000000964
état	Publié - 1 mai 2005

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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",

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AU - De Bouard, Anne

AU - Debussche, Arnaud

PY - 2005/5/1

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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

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