REGULARITY OF ALMOST PERIODIC MODULO SCALING SOLUTIONS FOR MASS-CRITICAL NLS AND APPLICATIONS

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	REGULARITY OF ALMOST PERIODIC MODULO SCALING SOLUTIONS FOR MASS-CRITICAL NLS AND APPLICATIONS
	Li, Dong 1; Zhang, Xiaoyi 2
	2010
发表期刊	ANALYSIS & PDE
ISSN	1948-206X
卷号	3 期号:2 页码:175-195
摘要	We consider the L(x)(2) solution u to mass-critical NLS iu(t) + Delta u = +/-vertical bar u vertical bar(4/d)u. We prove that in dimensions d >= 4, if the solution is spherically symmetric and is almost periodic modulo scaling, then it must lie in H(x)(1 + epsilon) for some epsilon > 0. Moreover, the kinetic energy of the solution is localized uniformly in time. One important application of the theorem is a simplified proof of the scattering conjecture for mass-critical NLS without reducing to three enemies. As another important application, we establish a Liouville type result for L(x)(2) initial data with ground state mass. We prove that if a radial L(x)(2) solution to focusing mass-critical problem has the ground state mass and does not scatter in both time directions, then it must be global and coincide with the solitary wave up to symmetries. Here the ground state is the unique, positive, radial solution to elliptic equation Delta Q - Q + Q(1+4/d) = 0. This is the first rigidity type result in scale invariant space L(x)(2).
关键词	Schrodinger equation mass-critical
语种	英语
资助项目	Mathematics Department of the University of Iowa ; NSF[DMS-0908032] ; University of Iowa ; Alfred P. Sloan Research Fellowship ; Project 973 in China
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000281884800003
出版者	MATHEMATICAL SCIENCE PUBL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10561
专题	中国科学院数学与系统科学研究院
通讯作者	Li, Dong
作者单位	1.Univ Iowa, Dept Math, Iowa City, IA 52240 USA 2.Acad Math & Syst Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Li, Dong,Zhang, Xiaoyi. REGULARITY OF ALMOST PERIODIC MODULO SCALING SOLUTIONS FOR MASS-CRITICAL NLS AND APPLICATIONS[J]. ANALYSIS & PDE,2010,3(2):175-195.
APA	Li, Dong,&Zhang, Xiaoyi.(2010).REGULARITY OF ALMOST PERIODIC MODULO SCALING SOLUTIONS FOR MASS-CRITICAL NLS AND APPLICATIONS.ANALYSIS & PDE,3(2),175-195.
MLA	Li, Dong,et al."REGULARITY OF ALMOST PERIODIC MODULO SCALING SOLUTIONS FOR MASS-CRITICAL NLS AND APPLICATIONS".ANALYSIS & PDE 3.2(2010):175-195.