On the rigidity of solitary waves for the focusing mass-critical NLS in dimensions d >= 2

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	On the rigidity of solitary waves for the focusing mass-critical NLS in dimensions d >= 2
其他题名	On the rigidity of solitary waves for the focusing mass-critical NLS in dimensions d≥2
	Li Dong 1; Zhang XiaoYi 2
	2012
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	55 期号:2 页码:385-434
摘要	For the focusing mass-critical NLS iu(t) + Delta u = \|u\|(4/d) u, it is conjectured that the only global non-scattering solution with ground state mass must be a solitary wave up to symmetries of the equation. In this paper, we settle the conjecture for H-x(1) initial data in dimensions d = 2,3 with spherical symmetry and d >= 4 with certain splitting-spherically symmetric initial data.
其他摘要	For the focusing mass-critical NLS iu_t + △u =-\|u\|~(4/d) u,it is conjectured that the only global nonscattering solution with ground state mass must be a solitary wave up to symmetries of the equation.In this paper,we settle the conjecture for H_x~1 initial data in dimensions d = 2,3 with spherical symmetry and d ≥ 4 with certain splitting-spherically symmetric initial data.
关键词	NONLINEAR SCHRODINGER-EQUATION DISPERSIVE EVOLUTION-EQUATIONS BLOW-UP SOLUTIONS CRITICAL POWER CAUCHY-PROBLEM GROUND-STATES SINGULARITIES UNIQUENESS STABILITY Schrodinger equation mass critical rigidity
收录类别	CSCD
语种	英语
资助项目	[National Science Foundation] ; [UBC] ; [Alfred P. Sloan fellowship]
CSCD记录号	CSCD:4537847
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/57126
专题	中国科学院数学与系统科学研究院
作者单位	1.University British Columbia, Dept Math, Vancouver, BC V6T 1Z3, Canada 2.中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Li Dong,Zhang XiaoYi. On the rigidity of solitary waves for the focusing mass-critical NLS in dimensions d >= 2[J]. SCIENCE CHINA-MATHEMATICS,2012,55(2):385-434.
APA	Li Dong,&Zhang XiaoYi.(2012).On the rigidity of solitary waves for the focusing mass-critical NLS in dimensions d >= 2.SCIENCE CHINA-MATHEMATICS,55(2),385-434.
MLA	Li Dong,et al."On the rigidity of solitary waves for the focusing mass-critical NLS in dimensions d >= 2".SCIENCE CHINA-MATHEMATICS 55.2(2012):385-434.