Energy-Critical NLS with Quadratic Potentials

doi:10.1080/03605300903328109

	Energy-Critical NLS with Quadratic Potentials
	Killip, Rowan 1; Visan, Monica 1,2; Zhang, Xiaoyi 3
刊名	COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
	2009
卷号	34 期号:12 页码:1531-1565
关键词	Energy critical Nonlinear Schrodinger equation
ISSN号	0360-5302
DOI	10.1080/03605300903328109
英文摘要	We consider the defocusing [image omitted]-critical nonlinear Schrodinger equation in all dimensions (n epsilon 3) with a quadratic potential [image omitted]. We show global well-posedness for radial initial data obeying delta u0(x), xu0(x)L2. In view of the potential V, this is the natural energy space. In the repulsive case, we also prove scattering. We follow the approach pioneered by Bourgain and Tao in the case of no potential; indeed, we include a proof of their results that incorporates a couple of simplifications discovered while treating the problem with quadratic potential.
资助项目	National Science Foundation
WOS研究方向	Mathematics
语种	英语
出版者	TAYLOR & FRANCIS INC
WOS记录号	WOS:000274422000001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/8731]
专题	中国科学院数学与系统科学研究院
通讯作者	Visan, Monica
作者单位	1.Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA 2.Inst Adv Study, Princeton, NJ 08540 USA 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Killip, Rowan,Visan, Monica,Zhang, Xiaoyi. Energy-Critical NLS with Quadratic Potentials[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,2009,34(12):1531-1565.
APA	Killip, Rowan,Visan, Monica,&Zhang, Xiaoyi.(2009).Energy-Critical NLS with Quadratic Potentials.COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,34(12),1531-1565.
MLA	Killip, Rowan,et al."Energy-Critical NLS with Quadratic Potentials".COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 34.12(2009):1531-1565.