Wave breaking and global existence for a weakly dissipative generalized two-component μμ-Hunter–Saxton system

In this paper, we study the wave-breaking phenomena and global existence for a weakly dissipative generalized two-component μμ-Hunter–Saxton system in the periodic setting. We first establish local well-posedness for the generalized system. We obtain a wave-breaking criterion for solutions and results of wave-breaking solutions with certain initial profiles. We also determine the exact blow-up rate of strong solutions and present a lower bound of the lifespan. Finally, we give a sufficient condition for global solutions.