Non-uniform dependence on initial data for the CH equation on the line
Analysis of PDEs
2010-09-24 v1
Abstract
We show the lack of uniform continuity of the flow map for the Camassa-Holm equation on the line, in the Sobolev spaces of index s > 3/2.
Cite
@article{arxiv.1009.4685,
title = {Non-uniform dependence on initial data for the CH equation on the line},
author = {A. Alexandrou Himonas and Carlos Kenig},
journal= {arXiv preprint arXiv:1009.4685},
year = {2010}
}
Comments
This is a corrected version of the paper that appeared in Diff. and Int. Eqns. 22 (2009), 201-224. We are indebted to Yanggeng Fu for pointing out that our argument only applies in the range s > 3/2 and not in the range s > 1 as originally stated