| Abstract: |
| 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. |
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