DMCA
Resonant decompositions and the I-method for cubic nonlinear Schrödinger
| Venue: | on R 2 . Disc. Cont. Dynam. Systems A |
| Citations: | 28 - 4 self |
BibTeX
@ARTICLE{Colliander_resonantdecompositions,
author = {J. Colliander and M. Keel and G. Staffilani and H. Takaoka and T. Tao},
title = {Resonant decompositions and the I-method for cubic nonlinear Schrödinger},
journal = {on R 2 . Disc. Cont. Dynam. Systems A},
year = {},
pages = {2008}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
Abstract. The initial value problem for the cubic defocusing nonlinear Schrödinger equation i∂tu + ∆u = |u | 2 u on the plane is shown to be globally well-posed for initial data in H s (R 2) provided s> 1/2. The proof relies upon an almost conserved quantity constructed using multilinear correction terms. The main new difficulty is to control the contribution of resonant interactions to these correction terms. The resonant interactions are significant due to the multidimensional setting of the problem and some orthogonality issues which arise. 1.
