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

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