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A sine-type Camassa-Holm equation: local well-posedness, Hölder continuity, and wave-breaking analysis

A sine-type Camassa-Holm equation: local well-posedness, Hölder continuity, and wave-breaking... In this paper, we explore the effect of sine-type higher-order nonlinearity on the dispersive dynamics by considering the Cauchy problem for a sine-type Camassa-Holm (alias sine-CH) equation, which is a higher-order generalization of the remarkable CH equation, and also admits the peakon solution. Some main results are presented containing the local well-posedness for strong solutions in subcritical or critical Besov spaces, Hölder continuity of the data-to-solution map, the blow-up criterion and the precise blow-up quantity in Sobolev space, and a sufficient condition with regard to the initial data ensuring the occurance of the wave-breaking phenomenon. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Monatshefte für Mathematik Springer Journals

A sine-type Camassa-Holm equation: local well-posedness, Hölder continuity, and wave-breaking analysis

Monatshefte für Mathematik , Volume OnlineFirst – Jan 18, 2022

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2022
ISSN
0026-9255
eISSN
1436-5081
DOI
10.1007/s00605-022-01670-9
Publisher site
See Article on Publisher Site

Abstract

In this paper, we explore the effect of sine-type higher-order nonlinearity on the dispersive dynamics by considering the Cauchy problem for a sine-type Camassa-Holm (alias sine-CH) equation, which is a higher-order generalization of the remarkable CH equation, and also admits the peakon solution. Some main results are presented containing the local well-posedness for strong solutions in subcritical or critical Besov spaces, Hölder continuity of the data-to-solution map, the blow-up criterion and the precise blow-up quantity in Sobolev space, and a sufficient condition with regard to the initial data ensuring the occurance of the wave-breaking phenomenon.

Journal

Monatshefte für MathematikSpringer Journals

Published: Jan 18, 2022

Keywords: Sine-type Camassa-Holm equation; Well-posedness; Hölder continuity; Blow-up criterion and quantity; Wave breaking; 35B30; 35G25; 35L05; 35Q53

References