Global well-posedness and blow-up for the hartree equation
© 2017 Wuhan Institute of Physics and Mathematics For 2 < ? < min {4,n}, we consider the focusing Hartree equation iu t +?u+(|x| -? *|u| 2 )u=0, x ? R n .Let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of - ? Q + Q = (|x| -?...
| Main Authors: | , , , |
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| Format: | Journal Article |
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Elsevier BV
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/58257 |
| _version_ | 1848760214433562624 |
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| author | YANG, L. LI, X. Wu, Yong Hong Caccetta, Louis |
| author_facet | YANG, L. LI, X. Wu, Yong Hong Caccetta, Louis |
| author_sort | YANG, L. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 2017 Wuhan Institute of Physics and Mathematics For 2 < ? < min {4,n}, we consider the focusing Hartree equation iu t +?u+(|x| -? *|u| 2 )u=0, x ? R n .Let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of - ? Q + Q = (|x| -? *|Q| 2 )Q. Guo and Wang [Z. Angew. Math. Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of (0.1) ifM[u] 1-s c E[u] s c < M[Q] 1-s c E[Q] s c (s c =[Formula presented]). In this paper, we consider the complementary caseM[u] 1-s c E[u] s c = M[Q] 1-s c E[Q] s c and obtain a criteria on blow-up and global existence for the Hartree equation (0.1). |
| first_indexed | 2025-11-14T10:12:13Z |
| format | Journal Article |
| id | curtin-20.500.11937-58257 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:12:13Z |
| publishDate | 2017 |
| publisher | Elsevier BV |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-582572017-11-24T05:47:20Z Global well-posedness and blow-up for the hartree equation YANG, L. LI, X. Wu, Yong Hong Caccetta, Louis © 2017 Wuhan Institute of Physics and Mathematics For 2 < ? < min {4,n}, we consider the focusing Hartree equation iu t +?u+(|x| -? *|u| 2 )u=0, x ? R n .Let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of - ? Q + Q = (|x| -? *|Q| 2 )Q. Guo and Wang [Z. Angew. Math. Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of (0.1) ifM[u] 1-s c E[u] s c < M[Q] 1-s c E[Q] s c (s c =[Formula presented]). In this paper, we consider the complementary caseM[u] 1-s c E[u] s c = M[Q] 1-s c E[Q] s c and obtain a criteria on blow-up and global existence for the Hartree equation (0.1). 2017 Journal Article http://hdl.handle.net/20.500.11937/58257 10.1016/S0252-9602(17)30049-8 Elsevier BV restricted |
| spellingShingle | YANG, L. LI, X. Wu, Yong Hong Caccetta, Louis Global well-posedness and blow-up for the hartree equation |
| title | Global well-posedness and blow-up for the hartree equation |
| title_full | Global well-posedness and blow-up for the hartree equation |
| title_fullStr | Global well-posedness and blow-up for the hartree equation |
| title_full_unstemmed | Global well-posedness and blow-up for the hartree equation |
| title_short | Global well-posedness and blow-up for the hartree equation |
| title_sort | global well-posedness and blow-up for the hartree equation |
| url | http://hdl.handle.net/20.500.11937/58257 |