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

Research paper by Anne de Bouard, Arnaud Debussche

Indexed on: 29 Jun '05Published on: 29 Jun '05Published in: Mathematics - Probability



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 Schrodinger 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.