A Note on the Generalized Camassa-Holm Equation

الملخص EN

We study the generalized Camassa-Holm equation which contains the Camassa-Holm (CH) equation and Novikov equation as special cases with the periodic boundary condition.

We get a blow-up scenario and obtain the global existence of strong and weak solutions under suitable assumptions, respectively.

Then, we construct the periodic peaked solutions and apply them to prove the ill-posedness in H s with s < 3 / 2 .