The Annals of Probability

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

Arnaud Debussche and Anne de Bouard

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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.

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Ann. Probab., Volume 33, Number 3 (2005), 1078-1110.

First available in Project Euclid: 6 May 2005

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Zentralblatt MATH identifier

Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 76B35 60H30: Applications of stochastic analysis (to PDE, etc.) 60J60: Diffusion processes [See also 58J65]

Nonlinear Schrödinger equations stochastic partial differential equations white noise blow-up variance identity support theorem


de Bouard, Anne; Debussche, Arnaud. Blow-up for the stochastic nonlinear Schrödinger equation with multiplicative noise. Ann. Probab. 33 (2005), no. 3, 1078--1110. doi:10.1214/009117904000000964.

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