On the Cauchy problem of a periodic 2-component μμ-Hunter–Saxton system

In this paper, we study the Cauchy problem of a periodic 2-component μμ-Hunter–Saxton system. We first establish the local well-posedness for the periodic 2-component μμ-Hunter–Saxton system by Kato’s semigroup theory. Then, we derive the precise blow-up scenario for strong solutions to the system. Moreover, we present some blow-up results for strong solutions to the system. Finally, we give a global existence result to the system.