Blow-up for the stochastic nonlinear Schrodinger 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 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.

Published at http://dx.doi.org/10.1214/009117904000000964 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)