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

TL;DR

This paper investigates the periodic 2-component μ-Hunter-Saxton system, establishing local well-posedness, blow-up scenarios, and conditions for global existence of solutions.

Contribution

It provides the first comprehensive analysis of well-posedness, blow-up behavior, and global existence for this specific 2-component μ-Hunter-Saxton system.

Findings

Local well-posedness established using Kato's semigroup theory

Precise blow-up scenarios identified for strong solutions

Global existence conditions derived

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.