On the Cauchy problem of a periodic 2-component $μ$-Hunter-Saxton equation

Jingjing Liu, Zhaoyang Yin

Published 2010-12-24, updated 2011-03-25Version 2

In this paper, we study the Cauchy problem of a periodic 2-component $\mu$-Hunter-Saxton system. We first establish the local well-posedness for the periodic 2-component $\mu$-Hunter-Saxton system by Kato's semigroup theory. Then, we derive precise blow-up scenarios for strong solutions to the system. Moreover, we present a blow-up result for strong solutions to the system. Finally, we give a global existence result to the system.