In this paper, we study the wave-breaking phenomena and global existence for the generalized two-component Hunter-Saxton system in the periodic setting. We first establish local well-posedness for the generalized two-component Hunter-Saxton 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. Finally, we give a sufficient condition for global solutions. © 2012 Elsevier Inc.
Moon, B., & Liu, Y. (2012). Wave breaking and global existence for the generalized periodic two-component Hunter-Saxton system. Journal of Differential Equations, 253(1), 319–355. https://doi.org/10.1016/j.jde.2012.02.011