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

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-de Vries model, we demonstrate conditions on the initial data that lead to finite time blow-up of certain solutions. (C) 2000 Academic Press.