On the Well-Posedness for Stochastic Schrodinger Equations with Quadratic Potential  

作　　者：Daoyuan FANG Linzi ZHANG Ting ZHANG 

机构地区：[1]Department of Mathematics, Zhejiang University, Hangzhou 310027, China [2]Corresponding author. Department of Mathematics, Zhejiang University, Hangzhou 310027, ChinaCorresponding author. Department of Mathematics, Zhejiang University, Hangzhou 310027, ChinaCorresponding author. Department of Mathematics, Zhejiang University, Hangzhou 310027, ChinaCorresponding author. Department of Mathematics, Zhejiang University, Hangzhou 310027, ChinaCorresponding author. Department of Mathematics, Zhejiang University, Hangzhou 310027, ChinaCorresponding author. Department of Mathematics, Zhejiang University, Hangzhou 310027, China

出　　处：《Chinese Annals of Mathematics,Series B》2011年第5期711-728,共18页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (Nos. 10871175,10931007,10901137);the Zhejiang Provincial Natural Science Foundation of China (No. Z6100217);the Specialized ResearchFund for the Doctoral Program of Higher Education (No. 20090101120005)

摘　　要：The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI（R^n）, ｜·｜f ∈ L^2（R^n）}. When the nonlinearity is focusing and L2-supercritical, the authors give sufficient conditions for the solutions to blow up in finite time for both confining and repulsive potential. Especially for the repulsive case, the solution to the deterministic equation with the initial data satisfying the stochastic blow-up condition will also blow up in finite time. Thus, compared with the deterministic equation for the repulsive case, the blow-up condition is stronger on average, and depends on the regularity of the noise. If φ = 0, our results coincide with the ones for the deterministic equation.

关 键 词：Stochastic SchrSdinger equation WELL-POSEDNESS Blow up 

分 类 号：O175.29[理学—数学] TB24[理学—基础数学]