On the focusing mass critical problem in six dimensions with splitting spherically symmetric initial data

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	On the focusing mass critical problem in six dimensions with splitting spherically symmetric initial data
	Li, Dong 1; Zhang, Xiaoyi 1,2
	2010-12-01
发表期刊	DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS
ISSN	1548-159X
卷号	7 期号:4 页码:345-373
摘要	In this paper, we consider the six-dimensional focusing mass critical NLS: iu(t) + Delta u = -vertical bar u vertical bar(2/3) u with splitting-spherical initial data u(0)(x(1), ... x(6)) = u(0)(root x(1)(2) + x(2)(2) + x(3)(2), root x(4)(2) + x(5)(2) + x(6)(2)). we prove that any finite mass solution which is almost periodic modulo scaling in both time directions must have Sobolev regularity H(x)(1+). Moreover, the kinetic energy of the solution is localized around the spatial origin uniformly in time. As important applications of the results, we prove the scattering conjecture for solutions with mass smaller than that of the ground state. We also prove that any two-way non-scattering solution must be global and coincides with the solitary wave up to symmetries. Here the ground state is the unique positive, radial solution of the nonlinear elliptic equation Delta Q - Q + Q(5/3) = 0. To prove the smoothness of the solution, we use a new local iteration scheme which first appears in [19].
关键词	Focusing mass critical NLS Sobolev regularity scattering conjecture
语种	英语
资助项目	Mathematics Department of University of Iowa ; NSF[090832] ; Alfred P. Sloan Research Fellowship
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000287554600004
出版者	INT PRESS BOSTON, INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/9509
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 52246 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 focusing mass critical problem in six dimensions with splitting spherically symmetric initial data[J]. DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS,2010,7(4):345-373.
APA	Li, Dong,&Zhang, Xiaoyi.(2010).On the focusing mass critical problem in six dimensions with splitting spherically symmetric initial data.DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS,7(4),345-373.
MLA	Li, Dong,et al."On the focusing mass critical problem in six dimensions with splitting spherically symmetric initial data".DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS 7.4(2010):345-373.