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.
Publié le : 2005-05-14
Classification:
Nonlinear Schrödinger equations,
stochastic partial differential equations,
white noise,
blow-up,
variance identity,
support theorem,
35Q55,
60H15,
76B35,
60H30,
60J60
@article{1115386719,
author = {de Bouard, Anne and Debussche, Arnaud},
title = {Blow-up for the stochastic nonlinear Schr\"odinger equation with multiplicative noise},
journal = {Ann. Probab.},
volume = {33},
number = {1},
year = {2005},
pages = { 1078-1110},
language = {en},
url = {http://dml.mathdoc.fr/item/1115386719}
}
de Bouard, Anne; Debussche, Arnaud. Blow-up for the stochastic nonlinear Schrödinger equation with multiplicative noise. Ann. Probab., Tome 33 (2005) no. 1, pp. 1078-1110. http://gdmltest.u-ga.fr/item/1115386719/