Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrodinger equations of fourth order in dimensions d ≥ 9

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:251

Article

Miao, Changxing²  Xu, Guixiang²  Zhao, Lifeng¹ 

[1] Univ Sci & Technol China, Dept Math, Hefei 230026, Peoples R China

[2] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

关键词: Defocusing;    Energy-critical;    Fourth order Schrodinger equations;    Global well-posedness;    Scattering;   

DOI  :  10.1016/j.jde.2011.08.009

来源: Elsevier

【 摘 要 】

We consider the defocusing energy-critical nonlinear Schrodinger equation of fourth order iu(t) + Delta(2)u = -vertical bar u vertical bar(8/d-4)u. We prove that any finite energy solution is global and scatters both forward and backward in time in dimensions d >= 9. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free