Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data

dc.creatorMiao, Changxing
dc.creatorXu, Guixiang
dc.creatorZhao, Lifeng
dc.date2007-04-05
dc.date2007-04-15
dc.date.accessioned2026-07-07T10:08:18Z
dc.date.available2026-07-07T10:08:18Z
dc.descriptionWe consider the defocusing, $\dot{H}^1$-critical Hartree equation for the radial data in all dimensions $(n\geq 5)$. We show the global well-posedness and scattering results in the energy space. The new ingredient in this paper is that we first take advantage of the term $\displaystyle - \int_{I}\int_{|x|\leq A|I|^{1/2}}|u|^{2}Δ\Big(\frac{1}{|x|}\Big)dxdt$ in the localized Morawetz identity to rule out the possibility of energy concentration, instead of the classical Morawetz estimate dependent of the nonlinearity.
dc.description23 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/0704.0665
dc.identifierhttp://arxiv.org/abs/0704.0665
dc.identifierJournal of Functional Analysis 253 (2007)605-627
dc.identifierdoi:10.1016/j.jfa.2007.09.008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170949
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.subject35Q40, 35Q55, 47J35
dc.titleGlobal well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data
dc.typetext

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