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...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.展开更多
基金Supported by NSFC (10871175,10931007,10901137)Zhejiang Provincial Natural Science Foundation of China (Z6100217)SRFDP (20090101120005)
文摘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.