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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.