The two-component μ-Hunter-Saxton system is considered in the spatially periodic setting. Firstly, two wave-breaking criteria are derived by employing the transport equation theory and the localization analysis method. Secondly, a sufficient condition of the blow-up solutions is established by using the classic method. The results obtained in this paper are new and different from those in previous works.
Keywords: Blow-up phenomena; Two-component μ-Hunter–Saxton system; Wave-breaking criteria.