A Note on the Generalized Camassa-Holm Equation - Yun Wu; Ping Zhao (Journal of Function Spaces, 2014)
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 Hs with s<3/2.