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

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

2008-07-04

arxiv.org/abs/0807.0692v2

J. Diff. Equ. Vol. 251, (2011) 3381-3402

Mathematics

Analysis of PDEs

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

Scientific paper

10.1016/j.jde.2011.08.009

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 $d\geq9$.

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