Multilinear Eigenfunction Estimates And Global Existence For The Three Dimensional Nonlinear SchrÖdinger Equations
| dc.creator | Burq, N. | |
| dc.creator | Gerard, P. | |
| dc.creator | Tzvetkov, N. | |
| dc.date | 2004-09-01 | |
| dc.date | 2005-01-27 | |
| dc.date.accessioned | 2026-07-07T05:11:43Z | |
| dc.date.available | 2026-07-07T05:11:43Z | |
| dc.description | 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. | |
| dc.description | Lemma 4.6 in the previous version was false, we made slight modifications to use only a weaker version of this lemma | |
| dc.identifier | https://arxiv.org/abs/math/0409015 | |
| dc.identifier | http://arxiv.org/abs/math/0409015 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72341 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q55, 35BXX, 37K05, 37L50, 81Q20 | |
| dc.title | Multilinear Eigenfunction Estimates And Global Existence For The Three Dimensional Nonlinear SchrÖdinger Equations | |
| dc.type | text |