The spatially periodic Cauchy problem for a generalized two-component μμ-Camassa–Holm system

Considered herein is the Cauchy problem of a generalized two-component μμ-Camassa–Holm (μμ-CH) system in the periodic setting. After the local well-posedness result is established, we first obtain a wave breaking criterion for solutions. Based on which, several blow-up data and blow up rate for strong solutions are also provided afterwards. Finally, a sufficient condition guaranteeing the global existence of strong solutions is determined.