On the Cauchy problem for a periodic rotation-two-component μ-Hunter–Saxton system.

A new rotation-two-component -Hunter–Saxton system is considered in the spatially periodic setting. The local well-posedness for the system is established by Kato theory. Two wave-breaking criteria and the sufficient conditions of blow-up solution are derived by relying on the Riccati differential equation and localization analysis. In addition, the Lyapunov function method is used to prove the existence of global solutions under certain conditions. [ABSTRACT FROM AUTHOR]