On the well-posedness for stochastic fourth-order Schrdinger equations  

作　　者：FANG Dao-yuan ZHANG Lin-zi ZHANG Ting 

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

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2011年第3期307-318,共12页高校应用数学学报（英文版）（B辑）

基　　金：Supported by NSFC (10871175,10931007,10901137);Zhejiang Provincial Natural Science Foundation of China (Z6100217);SRFDP (20090101120005)

摘　　要：The influence of the random perturbations on the fourth-order nonlinear SchrSdinger equations,iut＋△^2u＋ε△u＋λ｜u｜^p-1u=ξ,（t,x）∈R^＋×R^n,n≥1,ε∈{-1,0,＋1},is investigated in this paper. The local well-posedness in the energy space H^2（R^n） are proved for p 〉n＋4/n＋2,and p≤2^#-1 if n≥5.Global existence is also derived for either defocusing or focusing L^2-subcritical nonlinearities.The influence of the random perturbations on the fourth-order nonlinear SchrSdinger equations,iut＋△^2u＋ε△u＋λ｜u｜^p-1u=ξ,（t,x）∈R^＋×R^n,n≥1,ε∈{-1,0,＋1},is investigated in this paper. The local well-posedness in the energy space H^2（R^n） are proved for p 〉n＋4/n＋2,and p≤2^#-1 if n≥5.Global existence is also derived for either defocusing or focusing L^2-subcritical nonlinearities.

关 键 词：Stochastic fourth-order Schrodinger equation WELL-POSEDNESS global existence 

分 类 号：O175.2[理学—数学] TP273.2[理学—基础数学]