%0 Journal Article %T Global weak solutions for a periodic two-component $¦Ì$-Hunter-Saxton system %A Jingjing Liu %A Zhaoyang Yin %J Mathematics %D 2010 %I arXiv %X This paper is concerned with global existence of weak solution for a periodic two-component $\mu$-Hunter-Saxton system. We first derive global existence for strong solutions to the system with smooth approximate initial data. Then, we show that the limit of approximate solutions is a global weak solution of the two-component $\mu$-Hunter-Saxton system. %U http://arxiv.org/abs/1012.5452v3