Sharp Global well-posedness for KdV and modified KdV on $\R$ and $\T$
Analysis of PDEs
2007-05-23 v2
Abstract
The initial value problems for the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations under periodic and decaying boundary conditions are considered. These initial value problems are shown to be globally well-posed in all -based Sobolev spaces where local well-posedness is presently known, apart from the endpoint for mKdV. The result for KdV relies on a new method for constructing almost conserved quantities using multilinear harmonic analysis and the available local-in-time theory. Miura's transformation is used to show that global well-posedness of modified KdV is implied by global well-posedness of the standard KdV equation.
Keywords
Cite
@article{arxiv.math/0110045,
title = {Sharp Global well-posedness for KdV and modified KdV on $\R$ and $\T$},
author = {J. Colliander and M. Keel and G. Staffilani and H. Takaoka and T. Tao},
journal= {arXiv preprint arXiv:math/0110045},
year = {2007}
}
Comments
submitted to JAMS