The cubic nonlinear Schrödinger equation in two dimensions with radial data

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dc.creatorKillip, Rowan
dc.creatorTao, Terence
dc.creatorVisan, Monica
dc.date2007-07-21
dc.date2008-03-04
dc.date.accessioned2026-07-07T09:24:09Z
dc.date.available2026-07-07T09:24:09Z
dc.descriptionWe establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation $iu_t + Δu = \pm |u|^2 u$ for large spherically symmetric L^2_x(\R^2) initial data; in the focusing case we require, of course, that the mass is strictly less than that of the ground state. As a consequence, we deduce that in the focusing case, any spherically symmetric blowup solution must concentrate at least the mass of the ground state at the blowup time. We also establish some partial results towards the analogous claims in other dimensions and without the assumption of spherical symmetry.
dc.description49 pages, no figures, submitted, Annals of Math. Various corrections
dc.identifierhttps://arxiv.org/abs/0707.3188
dc.identifierhttp://arxiv.org/abs/0707.3188
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155994
dc.subjectAnalysis of PDEs
dc.subject35Q55
dc.titleThe cubic nonlinear Schrödinger equation in two dimensions with radial data
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