Remarks on the well-posedness of Camassa-Holm type equations in Besov spaces

In this paper, we prove the solution map of the Cauchy problem of Camassa-Holm type equations depends continuously on the initial data in nonhomogeneous Besov spaces in the sense of Hadamard by using the Littlewood-Paley theory and the method introduced by Kato [37] and Danchin [21].