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/lp/springer-journals/a-sine-type-camassa-holm-equation-local-well-posedness-h-lder-mP2rY5INme
- 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 Mathematik – Springer 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
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