On the local well-posedness of the Cauchy problem for a modified two-component Camassa-Holm system in Besov spaces (Q457894)

Summary: We consider the Cauchy problem for an integrable modified two-component Camassa-Holm system with cubic nonlinearity. By using the Littlewood-Paley decomposition, nonhomogeneous Besov spaces, and a priori estimates for linear transport equation, we prove that the Cauchy problem is locally well-posed in Besov spaces \(B_{p,r}^s\) with \(1 \leq p\), \(1 \leq p\), \(r\leq + \infty\) and \(s > \max \{2+(1/p),5/2\}\).