Ill-posedness for the Camassa-Holm and related equations in Besov spaces

Abstract

In this paper, we give a construction of u0∈Bp,∞σ such that the corresponding solution to the Camassa-Holm equation starting from u0 is discontinuous at t=0 in the metric of Bp,∞σ, which implies the ill-posedness for this equation in Bp,∞σ. We also apply our method to the b-equation and Novikov equation.