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

被引：69
作者：
De Bouard, A
Debussche, A
机构：
[1] CNRS, F-91405 Orsay, France
[2] Univ Paris 11, UMR 8628, F-91405 Orsay, France
[3] ENS Cachan, Antenne Bretagne, F-35170 Bruz, France
来源：
ANNALS OF PROBABILITY | 2005年 / 33卷 / 03期
关键词：
nonlinear Schrodinger equations; stochastic partial differential equations; white noise; blow-up; variance identity; support theorem;
D O I：
10.1214/009117904000000964
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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.
引用
收藏
页码：1078 / 1110
页数：33
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