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

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We 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.
Lemma 4.6 in the previous version was false, we made slight modifications to use only a weaker version of this lemma

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Analysis of PDEs, 35Q55, 35BXX, 37K05, 37L50, 81Q20

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http://salesiana.dossiersoluciones.com/handle/123456789/72341

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0409015
 http://arxiv.org/abs/math/0409015

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arXiv