KdV and Almost Conservation Laws
Analysis of PDEs
2007-05-23 v1
Abstract
This short survey paper is concerned with a new method to prove global well-posedness results for dispersive equations below energy spaces, namely for the Schr\"odinger equation and for the KdV equation. The main ingredient of this method is the definition of a family of what we call almost conservation laws. In particular we analyze the Korteweg-de Vries initial value problem and we illustrate in general terms how the ``algorithm'' that we use to formally generate almost conservation laws can be used to recover the infinitely many conserved integrals that make the KdV an integrable system.
Keywords
Cite
@article{arxiv.math/0204014,
title = {KdV and Almost Conservation Laws},
author = {Gigliola Staffilani},
journal= {arXiv preprint arXiv:math/0204014},
year = {2007}
}
Comments
15 pages. This paper will appear in the AMS Proceedings of the Conference on Harmonic Analysis held at Mt. Holyoke College, June 24 - July 5, 2001