Non-uniform dependence on initial data for the CH equation on the line
A.Alexandrou Himonas, Carlos Kenig
TL;DR
This paper demonstrates that the flow map for the Camassa-Holm equation on the real line is not uniformly continuous in Sobolev spaces with index s > 3/2, highlighting sensitivity to initial data.
Contribution
It establishes the non-uniform dependence of the solution flow on initial data for the CH equation in certain Sobolev spaces, a novel insight into its stability properties.
Findings
Flow map is not uniformly continuous in Sobolev spaces for s > 3/2
Shows sensitivity of solutions to initial data in the CH equation
Highlights limitations of stability in the solution flow
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.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Waves and Solitons · Nonlinear Partial Differential Equations