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Article: The focusing energy-critical Hartree equation
Title | The focusing energy-critical Hartree equation |
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Authors | |
Issue Date | 2009 |
Citation | Journal of Differential Equations, 2009, v. 246, n. 3, p. 1139-1163 How to Cite? |
Abstract | We consider the focusing energy-critical nonlinear Hartree equation i ut + Δ u = - (| x |-4 * | u |2) u. We proved that if a maximal-lifespan solution u : I × Rd → C satisfies supt ∈ I {norm of matrix} ∇ u (t) {norm of matrix}2 < {norm of matrix} ∇ W {norm of matrix}2, where W is the static solution of the equation, then the maximal-lifespan I = R, moreover, the solution scatters in both time directions. For spherically symmetric initial data, similar result has been obtained in [C. Miao, G. Xu, L. Zhao, Global wellposedness, scattering and blowup for the energy-critical, focusing Hartree equation in the radial case, Colloq. Math., in press]. The argument is an adaptation of the recent work of R. Killip and M. Visan [R. Killip, M. Visan, The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher, preprint] on energy-critical nonlinear Schrödinger equations. © 2008 Elsevier Inc. All rights reserved. |
Persistent Identifier | http://hdl.handle.net/10722/326613 |
ISSN | 2023 Impact Factor: 2.4 2023 SCImago Journal Rankings: 2.046 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Li, Dong | - |
dc.contributor.author | Miao, Changxing | - |
dc.contributor.author | Zhang, Xiaoyi | - |
dc.date.accessioned | 2023-03-31T05:25:14Z | - |
dc.date.available | 2023-03-31T05:25:14Z | - |
dc.date.issued | 2009 | - |
dc.identifier.citation | Journal of Differential Equations, 2009, v. 246, n. 3, p. 1139-1163 | - |
dc.identifier.issn | 0022-0396 | - |
dc.identifier.uri | http://hdl.handle.net/10722/326613 | - |
dc.description.abstract | We consider the focusing energy-critical nonlinear Hartree equation i ut + Δ u = - (| x |-4 * | u |2) u. We proved that if a maximal-lifespan solution u : I × Rd → C satisfies supt ∈ I {norm of matrix} ∇ u (t) {norm of matrix}2 < {norm of matrix} ∇ W {norm of matrix}2, where W is the static solution of the equation, then the maximal-lifespan I = R, moreover, the solution scatters in both time directions. For spherically symmetric initial data, similar result has been obtained in [C. Miao, G. Xu, L. Zhao, Global wellposedness, scattering and blowup for the energy-critical, focusing Hartree equation in the radial case, Colloq. Math., in press]. The argument is an adaptation of the recent work of R. Killip and M. Visan [R. Killip, M. Visan, The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher, preprint] on energy-critical nonlinear Schrödinger equations. © 2008 Elsevier Inc. All rights reserved. | - |
dc.language | eng | - |
dc.relation.ispartof | Journal of Differential Equations | - |
dc.title | The focusing energy-critical Hartree equation | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.jde.2008.05.013 | - |
dc.identifier.scopus | eid_2-s2.0-55649084151 | - |
dc.identifier.volume | 246 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 1139 | - |
dc.identifier.epage | 1163 | - |
dc.identifier.eissn | 1090-2732 | - |
dc.identifier.isi | WOS:000261775000010 | - |