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Article: Dynamics for the energy critical nonlinear Schrödinger equation in high dimensions
| Title | Dynamics for the energy critical nonlinear Schrödinger equation in high dimensions |
|---|---|
| Authors | |
| Keywords | Energy critical Ground state Schrödinger equation Variational structure |
| Issue Date | 2009 |
| Citation | Journal of Functional Analysis, 2009, v. 256, n. 6, p. 1928-1961 How to Cite? |
| Abstract | In [T. Duyckaerts, F. Merle, Dynamic of threshold solutions for energy-critical NLS, preprint, arXiv:0710.5915 [math.AP]], T. Duyckaerts and F. Merle studied the variational structure near the ground state solution W of the energy critical NLS and classified the solutions with the threshold energy E (W) in dimensions d = 3, 4, 5 under the radial assumption. In this paper, we extend the results to all dimensions d ≥ 6. The main issue in high dimensions is the non-Lipschitz continuity of the nonlinearity which we get around by making full use of the decay property of W. © 2008 Elsevier Inc. All rights reserved. |
| Persistent Identifier | http://hdl.handle.net/10722/326765 |
| ISSN | 2021 Impact Factor: 1.891 2020 SCImago Journal Rankings: 2.091 |
| ISI Accession Number ID |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Li, Dong | - |
| dc.contributor.author | Zhang, Xiaoyi | - |
| dc.date.accessioned | 2023-03-31T05:26:21Z | - |
| dc.date.available | 2023-03-31T05:26:21Z | - |
| dc.date.issued | 2009 | - |
| dc.identifier.citation | Journal of Functional Analysis, 2009, v. 256, n. 6, p. 1928-1961 | - |
| dc.identifier.issn | 0022-1236 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/326765 | - |
| dc.description.abstract | In [T. Duyckaerts, F. Merle, Dynamic of threshold solutions for energy-critical NLS, preprint, arXiv:0710.5915 [math.AP]], T. Duyckaerts and F. Merle studied the variational structure near the ground state solution W of the energy critical NLS and classified the solutions with the threshold energy E (W) in dimensions d = 3, 4, 5 under the radial assumption. In this paper, we extend the results to all dimensions d ≥ 6. The main issue in high dimensions is the non-Lipschitz continuity of the nonlinearity which we get around by making full use of the decay property of W. © 2008 Elsevier Inc. All rights reserved. | - |
| dc.language | eng | - |
| dc.relation.ispartof | Journal of Functional Analysis | - |
| dc.subject | Energy critical | - |
| dc.subject | Ground state | - |
| dc.subject | Schrödinger equation | - |
| dc.subject | Variational structure | - |
| dc.title | Dynamics for the energy critical nonlinear Schrödinger equation in high dimensions | - |
| dc.type | Article | - |
| dc.description.nature | link_to_subscribed_fulltext | - |
| dc.identifier.doi | 10.1016/j.jfa.2008.12.007 | - |
| dc.identifier.scopus | eid_2-s2.0-59849097711 | - |
| dc.identifier.volume | 256 | - |
| dc.identifier.issue | 6 | - |
| dc.identifier.spage | 1928 | - |
| dc.identifier.epage | 1961 | - |
| dc.identifier.eissn | 1096-0783 | - |
| dc.identifier.isi | WOS:000263759200011 | - |