Low-Regularity Solutions of the Periodic Camassa-Holm Equation

We prove local existence and uniqueness of weak solutions of the Camassa-Holm equation with periodic boundary conditions in various spaces of low-regularity which include the periodic peakons. The proof uses the connection of the Camassa-Holm equation with the geodesic flow on the diffeomorphism gro...

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Bibliographic Details
Published inCommunications in partial differential equations Vol. 32; no. 1; pp. 87 - 126
Main Authors Lellis, Camillo de, Kappeler, Thomas, Topalov, Peter
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 04.01.2007
Subjects
Camassa-Holm equation
Low-regularity solutions
Periodic peakons
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Summary:We prove local existence and uniqueness of weak solutions of the Camassa-Holm equation with periodic boundary conditions in various spaces of low-regularity which include the periodic peakons. The proof uses the connection of the Camassa-Holm equation with the geodesic flow on the diffeomorphism group of the circle with respect to the L 2 metric.
ISSN:0360-5302
1532-4133
DOI:10.1080/03605300601091470