Well-posedness and Blow-up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation
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.
- Publication:
-
Journal of Differential Equations
- Pub Date:
- March 2000
- DOI:
- 10.1006/jdeq.1999.3683
- Bibcode:
- 2000JDE...162...27L