Global wellposedness and scattering for the defocusing energy-critical nonlinear Schrodinger equations of fourth order in dimensions $d\geq9$

Abstract

We consider the defocusing energy-critical nonlinear Schr\"odinger equation of fourth order $iu_t+\Delta^2 u=-|u|^\frac{8}{d-4}u$. We prove that any finite energy solution is global and scatters both forward and backward in time in dimensions $d\geq9$.