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 language | English (US) |
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Pages (from-to) | 27-63 |
Number of pages | 37 |
Journal | Journal of Differential Equations |
Volume | 162 |
Issue number | 1 |
DOIs | |
State | Published - Mar 20 2000 |
Bibliographical note
Funding Information:1Supported in part by NSF Grant DMS 95-00931 and BSF Grant 94-00283.