Multilinear estimates for periodic KdV equations and applications
Analysis of PDEs
2007-05-23 v3
Abstract
We prove an endpoint multilinear estimate for the spaces associated to the periodic Airy equation. As a consequence we obtain sharp local well-posedness results for periodic generalized KdV equations, as well as some global well-posedness results below the energy norm. In particular we prove a multilinear estimate which completes the proof of global well-posedness for periodic KdV in a preceding paper (math.AP/0110045) down to the optimal regularity H^{-1/2}.
Cite
@article{arxiv.math/0110049,
title = {Multilinear estimates for periodic KdV equations and applications},
author = {Jim Colliander and Markus Keel and Gigliola Staffilani and Hideo Takaoka and Terence Tao},
journal= {arXiv preprint arXiv:math/0110049},
year = {2007}
}
Comments
39 pages. A correction to the Case 3 argument in Section 14