Global wellposedness and scattering for the defocusing energy-critical nonlinear Schrodinger equations of fourth order in dimensions $d\ge 9$

Abstract

We consider the defocusing energy-critical nonlinear Schrödinger equation of fourth order $i{u}_t+{\Delta }^{2}u=-|u{|}^{\frac{8}{d-4}}u$. We prove that any finite energy solution is global and scatters both forward and backward in time in dimensions $d\ge 9$.

23 pages, some errors in Proposition 5.1 and section 7 are fixed. Other typos are corrected

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• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
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• Global Well-posedness and scattering for fourth-order Schrödinger equations on waveguide manifolds
• On the decay property of the cubic fourth-order Schrödinger equation
• Global solutions for $H^s$-critical nonlinear biharmonic Schrödinger equation
• Global existence and scattering for a class of nonlinear fourth-order Schrödinger equation below the energy space
• Random data theory for the cubic fourth-order nonlinear Schrödinger equation