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DIVERGENT SOLUTIONS TO THE 5D HARTREE EQUATIONS
Cao, Daomin; Guo, Qing
2011
Source PublicationCOLLOQUIUM MATHEMATICUM
ISSN0010-1354
Volume125Issue:2Pages:255-287
AbstractWe 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.
KeywordHartree equation blow-up profile decomposition divergent solutions
DOI10.4064/cm125-2-10
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000299619900010
PublisherARS POLONA-RUCH
Citation statistics
Cited Times:6[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/12624
Collection应用数学研究所
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
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.
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