On the well-posedness for stochastic fourth-order Schrdinger equations

The influence of the random perturbations on the fourth-order nonlinear Schrdinger equations,iut+△2u+εu+λ|u| p-1u=ξ,(t,x) ∈R+×Rn,n≥1,ε∈{-1,0,+1},is investigated in this paper.The local well-posedness in the energy space H2(Rn) 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 L2-subcritical nonlinearities.