KMS Of Academy of mathematics and systems sciences, CAS
DIVERGENT SOLUTIONS TO THE 5D HARTREE EQUATIONS | |
Cao, Daomin; Guo, Qing | |
2011 | |
Source Publication | COLLOQUIUM MATHEMATICUM |
ISSN | 0010-1354 |
Volume | 125Issue:2Pages:255-287 |
Abstract | 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. |
Keyword | Hartree equation blow-up profile decomposition divergent solutions |
DOI | 10.4064/cm125-2-10 |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics |
WOS ID | WOS:000299619900010 |
Publisher | ARS POLONA-RUCH |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/12624 |
Collection | 应用数学研究所 |
Affiliation | Chinese 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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