ON THE RIGIDITY OF MINIMAL MASS SOLUTIONS TO THE FOCUSING MASS-CRITICAL NLS FOR ROUGH INITIAL DATA

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	ON THE RIGIDITY OF MINIMAL MASS SOLUTIONS TO THE FOCUSING MASS-CRITICAL NLS FOR ROUGH INITIAL DATA
	Li, Dong 1; Zhang, Xiaoyi 1,2
	2009-06-16
发表期刊	ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	1072-6691
页码	19
摘要	For the focusing mass-critical nonlinear Schrodinger equation iu(t)+ Delta u = -\|u\|(4/d)u, an important problem is to establish Liouville type results for solutions with ground state mass. Here the ground state is the positive solution to elliptic equation Delta Q-Q+Q(1+4d) = 0. Previous results in this direction were established in [12, 16, 17, 29] and they all require u(0) is an element of H(x)(1)(R(d)). In this paper, we consider the rigidity results for rough initial data u(0) is an element of H(x)(s)(R(d)) for any s > 0. We show that in dimensions d >= 4 and under the radial assumption, the only solution that does not scatter in both time directions (including the finite time blowup case) must be global and coincide with the solitary wave e(it)Q up to symmetries of the equation. The proof relies on a non-uniform local iteration scheme, the refined estimate involving the P(+/-) operator and a new smoothing estimate for spherically symmetric solutions.
关键词	Mass-critical nonlinear Schrodinger equation
语种	英语
资助项目	National Science Foundation[DMS-0635607] ; National Science Foundation[10601060] ; Mathematics Department of University of Iowa ; 973 in China
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000208184200003
出版者	TEXAS STATE UNIV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7821
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.Inst Adv Study, Princeton, NJ 08544 USA 2.Acad Math & Syst Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Li, Dong,Zhang, Xiaoyi. ON THE RIGIDITY OF MINIMAL MASS SOLUTIONS TO THE FOCUSING MASS-CRITICAL NLS FOR ROUGH INITIAL DATA[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS,2009:19.
APA	Li, Dong,&Zhang, Xiaoyi.(2009).ON THE RIGIDITY OF MINIMAL MASS SOLUTIONS TO THE FOCUSING MASS-CRITICAL NLS FOR ROUGH INITIAL DATA.ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS,19.
MLA	Li, Dong,et al."ON THE RIGIDITY OF MINIMAL MASS SOLUTIONS TO THE FOCUSING MASS-CRITICAL NLS FOR ROUGH INITIAL DATA".ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS (2009):19.