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arXiv:0807.0692 [math.AP]AbstractReferencesReviewsResources

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

Changxing Miao, Guixiang Xu, Lifeng Zhao

Published 2008-07-04, updated 2009-09-14Version 2

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 $d\geq9$.

Comments: 23 pages, some errors in Proposition 5.1 and section 7 are fixed. Other typos are corrected
Journal: J. Diff. Equ. Vol. 251, (2011) 3381-3402
Categories: math.AP, math-ph, math.MP
Subjects: 35Q40, 35Q55, 47J35
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