Abstract
In this paper, we consider the Cauchy problem for the generalized Camassa-Holm equation. By using the littlewood-Paley decomposition and nonhomogeneous Besov spaces, we prove that the Cauchy problem for the generalized Camassa-Holm equation is locally well posed in the Besov space with and which generalizes the local well-posedness result in [1]. We also establish the ill-posedness result of the generalized Camassa-Holm equation and give a blow-up criterion.
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