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

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

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