Classical solutions of the periodic Camassa—Holm equation View Full Text


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Article Info

DATE

2002-11

AUTHORS

G. Misiolek

ABSTRACT

We study the periodic Cauchy problem for the Camassa—Holm equation and prove that it is locally well-posed in the space of continuously differentiable functions on the circle. The approach we use consists in rewriting the equation and deriving suitable estimates which permit application of o.d.e. techniques in Banach spaces. We also describe results in fractional Sobolev Hs spaces and in Appendices provide a direct well-posedness proof for arbitrary real s > 3/2 based on commutator estimates of Kato and Ponce as well as include a derivation of the equation on the diffeomorphism group of the circle together with related curvature computations. More... »

PAGES

1080-1104

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/pl00012648

DOI

http://dx.doi.org/10.1007/pl00012648

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1021747716


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