Open Access
Translator Disclaimer
May 2005 Blow-up for the stochastic nonlinear Schrödinger equation with multiplicative noise
Arnaud Debussche, Anne de Bouard
Ann. Probab. 33(3): 1078-1110 (May 2005). DOI: 10.1214/009117904000000964

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.

Citation

Download Citation

Arnaud Debussche. Anne de Bouard. "Blow-up for the stochastic nonlinear Schrödinger equation with multiplicative noise." Ann. Probab. 33 (3) 1078 - 1110, May 2005. https://doi.org/10.1214/009117904000000964

Information

Published: May 2005
First available in Project Euclid: 6 May 2005

zbMATH: 1068.35191
MathSciNet: MR2135313
Digital Object Identifier: 10.1214/009117904000000964

Subjects:
Primary: 35Q55 , 60H15
Secondary: 60H30 , 60J60 , 76B35

Keywords: Blow-up , Nonlinear Schrödinger equations , Stochastic partial differential equations , Support theorem , variance identity , White noise

Rights: Copyright © 2005 Institute of Mathematical Statistics

JOURNAL ARTICLE
33 PAGES


SHARE
Vol.33 • No. 3 • May 2005
Back to Top