DIVERGENT SOLUTIONS TO THE 5D HARTREE EQUATIONS

doi:10.4064/cm125-2-10

CSpace > 应用数学研究所

	DIVERGENT SOLUTIONS TO THE 5D HARTREE EQUATIONS
	Cao, Daomin; Guo, Qing
	2011
发表期刊	COLLOQUIUM MATHEMATICUM
ISSN	0010-1354
卷号	125 期号:2 页码:255-287
摘要	We consider the Cauchy problem for the focusing Hartree equation iu(t) + Delta u + (vertical bar .vertical bar (3) * vertical bar u vertical bar(2))u = 0 in R-5 with initial data in H-1, and study the divergence property of infinite-variance and nonradial solutions. For the ground state solution of -Q + Delta Q + (vertical bar.vertical bar(-3) * vertical bar Q vertical bar(2)) Q = 0 in R-5, we prove that if u(0) is an element of H-1 satisfies M (u(0))E(u(0)) < M(Q)E(Q) and parallel to del u0 parallel to(2)parallel to u0 parallel to(2) > parallel to del Q parallel to(2)parallel to Q parallel to(2); then the corresponding solution u(t) either blows up in finite forward time, or exists globally for positive time and there exists a time sequence t(n) -> infinity such that parallel to del u(t(n))parallel to(2) -> infinity. A similar result holds for negative time.
关键词	Hartree equation blow-up profile decomposition divergent solutions
DOI	10.4064/cm125-2-10
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000299619900010
出版者	ARS POLONA-RUCH
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12624
专题	应用数学研究所
通讯作者	Cao, Daomin
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Cao, Daomin,Guo, Qing. DIVERGENT SOLUTIONS TO THE 5D HARTREE EQUATIONS[J]. COLLOQUIUM MATHEMATICUM,2011,125(2):255-287.
APA	Cao, Daomin,&Guo, Qing.(2011).DIVERGENT SOLUTIONS TO THE 5D HARTREE EQUATIONS.COLLOQUIUM MATHEMATICUM,125(2),255-287.
MLA	Cao, Daomin,et al."DIVERGENT SOLUTIONS TO THE 5D HARTREE EQUATIONS".COLLOQUIUM MATHEMATICUM 125.2(2011):255-287.