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

The local well-posedness and global solution for a modified periodic two-component Camassa–Holm system on the circle SS are established in the Sobolev space Hs×Hs−2Hs×Hs−2 with s>72, which are different from that of the two-component Camassa–Holm system.