The local well-posedness and global solution for a modified periodic two-component Camassa-Holm system (Q2338690)

The aim of this paper is to consider a modified periodic two-component Camassa-Holm system on the circle \(\mathcal{S}=\mathbb{R}/\mathbb{Z}\) of unit length. The local well-posedness and global solution for this system are established in the Sobolev space \(H^s\times H^{s-2}\) with \(s>72\), which are different from that of the two-component Camassa-Holm system.