Global well-posedness and scattering for the focusing energy-critical nonlinear Schrodinger equations of fourth order in the radial case

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:246

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: Focusing;    Energy-critical;    Radial;    Fourth-order Schrodinger equations;    Global well-posedness;    Scattering;   

DOI  :  10.1016/j.jde.2008.11.011

来源: Elsevier

【 摘 要 】

We consider the focusing energy-critical nonlinear Schrodinger equation Of fourth order iu(t) + Delta(2)u = vertical bar u vertical bar(8/d-4)u, d >= 5, We prove that if a maximal-lifespan radial solution u: I x R d, C obeys sup(t is an element of l) parallel to Delta u(t)parallel to(2) < parallel to Delta W parallel to(2), then it is global and scatters both forward and backward in time. Here W denotes the ground state, which is a stationary solution of the equation. In particular, if a Solution has both energy and kinetic energy less than those of the ground state W at some point in time, then the Solution is global and scatters. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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