On blow-up of solutions to the two-component π-Camassa–Holm system

We investigate Cauchy problem of the two-component π-Camassa–Holm system which arises from geodesic flow on a semidirect product Lie group of the circle. The precise blow-up scenarios of strong solutions are derived for the system. Then, several criteria to guarantee blow-up of strong solutions are presented. Finally, the exact blow-up rate is determined.