Multilinear Eigenfunction Estimates And Global Existence For The Three Dimensional Nonlinear SchrÖdinger Equations

dc.creatorBurq, N.
dc.creatorGerard, P.
dc.creatorTzvetkov, N.
dc.date2004-09-01
dc.date2005-01-27
dc.date.accessioned2026-07-07T05:11:43Z
dc.date.available2026-07-07T05:11:43Z
dc.descriptionWe study nonlinear Schrödinger equations, posed on a three dimensional Riemannian manifold $M$. We prove global existence of strong $H^1$ solutions on $M=S^3$ and $M=S^2\times S^1$ as far as the nonlinearity is defocusing and sub-quintic and thus we extend the results of Ginibre-Velo and Bourgain who treated the cases of the Euclidean space $\R^3$ and the flat torus $\T^3$ respectively. The main ingredient in our argument is a new set of multilinear estimates for spherical harmonics.
dc.descriptionLemma 4.6 in the previous version was false, we made slight modifications to use only a weaker version of this lemma
dc.identifierhttps://arxiv.org/abs/math/0409015
dc.identifierhttp://arxiv.org/abs/math/0409015
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72341
dc.subjectAnalysis of PDEs
dc.subject35Q55, 35BXX, 37K05, 37L50, 81Q20
dc.titleMultilinear Eigenfunction Estimates And Global Existence For The Three Dimensional Nonlinear SchrÖdinger Equations
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