On the wave-breaking phenomena and global existence for the periodic rotation-two-component Camassa-Holm system

Considered herein is the periodic rotation-two-component Camassa-Holm system, which can be derived from the f-plane governing equations for the geophysical water waves with a constant underlying current. The nonlocal nonlinearities on blow-up criteria and wave-breaking phenomena are established. Finally, a sufficient condition for global solutions is obtained by using a method of the Lyapunov function.