Blow-up for the stochastic nonlinear Schrodinger equations with quadratic potential and additive noise

被引：1

作者：

Meng, Lixin ^{[1
]}

Li, Jingyu ^{[1
]}

Tao, Jian ^{[1
]}

机构：

[1] NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

来源：

BOUNDARY VALUE PROBLEMS | 2015年

基金：

中国国家自然科学基金;

关键词：

stochastic Schrodinger equation; Bose-Einstein condensation; quadratic potential; white noise; blow-up; MULTIPLICATIVE NOISE;

D O I：

10.1186/s13661-015-0394-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the dynamics of a stochastic nonlinear Schrodinger equation with both a quadratic potential and an additive noise. We show that in both cases of repulsive potential and attractive one, any initial data with finite variance gives birth to a solution that blows up in arbitrarily small time. This is in contrast to the deterministic case when the potential is repulsive, where strong potentials could prevent the solutions from blowing up. Our result hence indicates that the additive noise rather than the potential dominates the dynamical behaviors of the solutions to the stochastic nonlinear Schrodinger equations.

引用

页数：18

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