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

Yi A. Li, Peter J. Olver

Research output: Contribution to journalArticlepeer-review

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Abstract

We establish local well-posedness in the Sobolev space Hs 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 languageEnglish (US)
Pages (from-to)27-63
Number of pages37
JournalJournal of Differential Equations
Volume162
Issue number1
DOIs
StatePublished - Mar 20 2000

Bibliographical note

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

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