Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equations of fourth order in dimensions [formula omitted

Abstract

We consider the defocusing energy-critical nonlinear Schrödinger equation of fourth order i u t + Δ 2 u = − | u | 8 d − 4 u . We prove that any finite energy solution is global and scatters both forward and backward in time in dimensions d ⩾ 9 .