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

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

2005-06-29

arxiv.org/abs/math/0506595v1

Annals of Probability 2005, Vol. 33, No. 3, 1078-1110

Mathematics

Probability

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

Scientific paper

10.1214/009117904000000964

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.

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