DMCA
Global well-posedness for a periodic nonlinear Schrödinger equation (2006)
| Venue: | in 1D and 2D, arXiv: math.AP/0602660v1 |
| Citations: | 11 - 2 self |
BibTeX
@INPROCEEDINGS{Silva06globalwell-posedness,
author = {Daniela De Silva and Nata ˇ Sa Pavlović and Gigliola Staffilani and Nikolaos Tzirakis},
title = {Global well-posedness for a periodic nonlinear Schrödinger equation},
booktitle = {in 1D and 2D, arXiv: math.AP/0602660v1},
year = {2006}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
Abstract. The initial value problem for the L 2 critical semilinear Schrödinger equation with periodic boundary data is considered. We show that the problem is globally well posed in H s (T d), for s> 4/9 and s> 2/3 in 1D and 2D respectively, confirming in 2D a statement of Bourgain in [3]. We use the “I-method”. This method allows one to introduce a modification of the energy functional that is well defined for initial data below the H 1 (T d) threshold. The main ingredient in the proof is a “refinement ” of the Strichartz’s estimates that hold true for solutions defined on the rescaled space, T d λ = R d /λZ d, d = 1, 2.
