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

Abstract

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.

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• An integrable shallow water equation with peaked solitons
• On an integrable two-component Camassa-Holm shallow water system
• Blow-up phenomena and global existence for a periodic two-component Hunter-Saxton system
• On the blow-up structure for the generalized periodic Camassa-Holm and Degasperis-Procesi equations