Blow-up of solutions to the nonlinear Schr$\bf{\ddot{O}}$dinger equations on standard N-sphere and hyperbolic N-space

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dc.creatorMa, Li
dc.creatorZhao, Lin
dc.date2007-01-07
dc.date.accessioned2026-07-07T07:39:09Z
dc.date.available2026-07-07T07:39:09Z
dc.descriptionIn this paper, we partially settle down the long standing open problem of the finite time blow-up property about the nonlinear Schr$\ddot{o}$dinger equations on some Riemannian manifolds like the standard 2-sphere $S^2$ and the hyperbolic 2-space $H^{2}(-1)$. Using the similar idea, we establish such blow-up results on higher dimensional standard sphere and hyperbolic $n$-space. Extensions to $n$-dimensional Riemannian warped product manifolds with $n\geq 2$ are also given.
dc.description19 pages
dc.identifierhttps://arxiv.org/abs/math/0701200
dc.identifierhttp://arxiv.org/abs/math/0701200
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/121340
dc.subjectClassical Analysis and ODEs
dc.subjectDifferential Geometry
dc.subject35J
dc.titleBlow-up of solutions to the nonlinear Schr$\bf{\ddot{O}}$dinger equations on standard N-sphere and hyperbolic N-space
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