Global weak solutions for a periodic two-component $\mu$-Hunter-Saxton system

TL;DR

This paper establishes the global existence of weak solutions for a periodic two-component $or$-Hunter-Saxton system, advancing understanding of its mathematical properties and solution behavior.

Contribution

It proves the existence of global weak solutions for the two-component $or$-Hunter-Saxton system, extending previous results on strong solutions.

Findings

Global weak solutions exist for the system.

Strong solutions can be approximated by smooth initial data.

Limit of approximate solutions yields a weak solution.

Abstract

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.