Non-uniform dependence on initial data for the CH equation on the line

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.

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