Non-Uniform Dependence for the Periodic CH Equation

We show that the solution map of the periodic CH equation is not uniformly continuous in Sobolev spaces with exponent greater than 3/2. This extends earlier results to the whole range of Sobolev exponents for which local well-posedness of CH is known. The crucial technical tools used in the proof of...

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Bibliographic Details
Published in:	Communications in partial differential equations Vol. 35; no. 6; pp. 1145 - 1162
Main Authors:	Alexandrou Himonas, A., Kenig, Carlos, Misiołek, Gerard
Format:	Journal Article
Language:	English
Published:	Philadelphia Taylor & Francis Group 01-06-2010 Taylor & Francis Ltd
Subjects:	Approximate solutions CH equation Commutator estimate Multiplier estimate Non-uniform dependence on initial data Partial differential equations Periodic Cauchy problem Sobolev spaces Well-posedness
Online Access:	Get full text
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Summary:	We show that the solution map of the periodic CH equation is not uniformly continuous in Sobolev spaces with exponent greater than 3/2. This extends earlier results to the whole range of Sobolev exponents for which local well-posedness of CH is known. The crucial technical tools used in the proof of this result are a sharp commutator estimate and a multiplier estimate in Sobolev spaces of negative index.
ISSN:	0360-5302 1532-4133
DOI:	10.1080/03605300903436746