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

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

2010-12-24

arxiv.org/abs/1012.5349v2

Mathematics

Analysis of PDEs

Scientific paper

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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