Global existence for the two-component Camassa-Holm system and the   modified two-component Camassa-Holm system
  The present work is mainly concerned with global existence for the two-component Camassa-Holm system and the modified two-component Camassa-Holm system. By discovering new conservative quantities of these systems, we prove several new global existence results for these two-component shallow water systems. 
Jingjing Liu, Zhaoyang Yin
math.AP