Minimal-mass blowup solutions of the mass-critical NLS

doi:10.1515/FORUM.2008.042

CSpace

	Minimal-mass blowup solutions of the mass-critical NLS
	Tao, Terence 1; Visan, Monica ; Zhang, Xiaoyi 2
	2008
发表期刊	FORUM MATHEMATICUM
ISSN	0933-7741
卷号	20 期号:5 页码:881-919
摘要	We consider the minimal mass m(0) required for solutions to the mass-critical nonlinear Schrodinger (NLS) equation iu(t) + Delta u = mu vertical bar mu vertical bar(boolean AND/d)u to blow up. If m(0) is finite, we show that there exists a minimal-mass solution blowing up (in the sense of an infinite spacetime norm) in both time directions, whose orbit in L(x)(2)(R(d)) is compact after quotienting out by the symmetries of the equation. A similar result is obtained for spherically symmetric solutions. Similar results were previously obtained by Keraani, [17], in dimensions 1, 2 and Begout and Vargas, [2], in dimensions d >= 3 for the mass-critical NLS and by Kenig and Merle, [18], in the energy-critical case. In a subsequent paper we shall use this compactness result to establish global existence and scattering in L(x)(2)(R(d)) for the defocusing NLS in three and higher dimensions with spherically symmetric data.
DOI	10.1515/FORUM.2008.042
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000261170700006
出版者	WALTER DE GRUYTER & CO
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6311
专题	中国科学院数学与系统科学研究院
通讯作者	Tao, Terence
作者单位	1.Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100864, Peoples R China
推荐引用方式 GB/T 7714	Tao, Terence,Visan, Monica,Zhang, Xiaoyi. Minimal-mass blowup solutions of the mass-critical NLS[J]. FORUM MATHEMATICUM,2008,20(5):881-919.
APA	Tao, Terence,Visan, Monica,&Zhang, Xiaoyi.(2008).Minimal-mass blowup solutions of the mass-critical NLS.FORUM MATHEMATICUM,20(5),881-919.
MLA	Tao, Terence,et al."Minimal-mass blowup solutions of the mass-critical NLS".FORUM MATHEMATICUM 20.5(2008):881-919.