Scattering for the focusing (H) over dot(1/2)-critical Hartree equation in energy space

doi:10.1016/j.na.2010.04.033

CSpace

	Scattering for the focusing (H) over dot(1/2)-critical Hartree equation in energy space
	Gao, Yanfang 1; Wu, Haigen 2,3
	2010-08-15
发表期刊	NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
ISSN	0362-546X
卷号	73 期号:4 页码:1043-1056
摘要	We investigate the focusing nonlinear Schrodinger equation (NLS) of Hartree type i partial derivative(t)u + Delta u = -(vertical bar . vertical bar(2-d) * vertical bar u vertical bar(2))u in R-5 with initial data in energy space H-1. If M[u(0)]E[u(0)] < M[Q]E[Q], parallel to u(0)parallel to(2)parallel to del u(0)parallel to(2) < parallel to Q parallel to(2)parallel to del Q parallel to(2). Then the solution with initial data u(0) is global and scatters. Here Q is the ground state solution. Moreover, we show that if M[u(0)]E[u(0)] < M[Q]E[Q], but parallel to u(0)parallel to(2)parallel to del u(0)parallel to(2) > parallel to Q parallel to(2)parallel to del Q parallel to(2), then the corresponding solution will blow up in finite time. The argument of this work is based on the linear profile decomposition, in the spirit of Kenig-Merle. (C) 2010 Elsevier Ltd. All rights reserved.
关键词	Hartree equation Scattering Profile decomposition Blow-up
DOI	10.1016/j.na.2010.04.033
语种	英语
资助项目	NNSF of China[10771052] ; NNSF of China[10801015] ; Xu Guozhi Postdoctoral Foundation
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000278546300019
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/9903
专题	中国科学院数学与系统科学研究院
通讯作者	Gao, Yanfang
作者单位	1.Jilin Univ, Inst Math, Changchun 130012, Peoples R China 2.Chinese Acad Sci, Inst Syst Sci, Beijing 100190, Peoples R China 3.Henan Polytech Univ, Sch Math, Jiaozuo 454000, Peoples R China
推荐引用方式 GB/T 7714	Gao, Yanfang,Wu, Haigen. Scattering for the focusing (H) over dot(1/2)-critical Hartree equation in energy space[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,2010,73(4):1043-1056.
APA	Gao, Yanfang,&Wu, Haigen.(2010).Scattering for the focusing (H) over dot(1/2)-critical Hartree equation in energy space.NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,73(4),1043-1056.
MLA	Gao, Yanfang,et al."Scattering for the focusing (H) over dot(1/2)-critical Hartree equation in energy space".NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 73.4(2010):1043-1056.