Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation

Yi A. Li; Peter J. Olver

doi:10.1006/jdeq.1999.3683

Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation

Yi A. Li, Peter J. Olver

Mathematics

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532 Scopus citations

Abstract

We establish local well-posedness in the Sobolev space H^s with any s>3/2 for an integrable nonlinearly dispersive wave equation arising as a model for shallow water waves known as the Camassa-Holm equation. However, unlike the more familiar Korteweg-deVries model, we demonstrate conditions on the initial data that lead to finite time blow-up of certain solutions.

Original language	English (US)
Pages (from-to)	27-63
Number of pages	37
Journal	Journal of Differential Equations
Volume	162
Issue number	1
DOIs	https://doi.org/10.1006/jdeq.1999.3683
State	Published - Mar 20 2000

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Funding Information:
1Supported in part by NSF Grant DMS 95-00931 and BSF Grant 94-00283.

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Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation

Abstract

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