On H 2-solutions for a Camassa-Holm type equation

Camassa-Holm type equations arise as models for the unidirectional propagation of shallow water waves over a flat bottom. They also describe finite length, small amplitude radial deformation waves in cylindrical compressible hyperelastic rods. Under appropriate assumption on the initial data, on the time T T , and on the coefficients of such equation, we prove the well-posedness of the classical solutions for the Cauchy problem.