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hal.structure.identifierInstitut de Mathématiques de Toulouse UMR5219 [IMT]
dc.contributor.authorRAPHAËL, Pierre
hal.structure.identifierLaboratoire de Mathématiques Appliquées de Bordeaux [MAB]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorSZEFTEL, Jérémie
dc.date.accessioned2024-04-04T02:42:00Z
dc.date.available2024-04-04T02:42:00Z
dc.date.issued2009
dc.identifier.issn0010-3616
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191205
dc.description.abstractEnWe consider the quintic nonlinear Schr ̈odinger equation in dimension N ≥ 3. This problem is energy critical in dimension N = 3 and energy super critical for N ≥ 4. We prove the existence of a radially symmetric blow up mechanism with L2 concentration along the unit sphere of RN . This singularity formation is moreover stable by smooth and radially symmetric perturbation of the initial data. This result extends the result obtained for N = 2 in [29] and is the first result of description of a singularity formation in the energy supercritical class for (NLS) type problems. Our main tool is the proof of the propagation of regularity outside the blow up sphere in the presence a so-called log-log type singularity.
dc.language.isoen
dc.publisherSpringer Verlag
dc.title.enStanding ring blow up solutions to the N-dimensional quintic nonlinear Schrödinger equation
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.journalCommunications in Mathematical Physics
bordeaux.pageA paraître
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00359368
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00359368v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Communications%20in%20Mathematical%20Physics&rft.date=2009&rft.spage=A%20para%C3%AEtre&rft.epage=A%20para%C3%AEtre&rft.eissn=0010-3616&rft.issn=0010-3616&rft.au=RAPHA%C3%8BL,%20Pierre&SZEFTEL,%20J%C3%A9r%C3%A9mie&rft.genre=article


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