Global weak solutions for a periodic two-component μ-Hunter-Saxton system

2010/12/25 by Jingjing Liu, Zhaoyang Yin, Liu, Jingjing +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.AP

paper · pdf · doi:10.48550/arxiv.1012.5452

openalex publication_date 2010/12/25 · arxiv created 2011/02/25 · arxiv updated 2011/02/28 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with global existence of weak solution for a periodic two-component μ-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 μ-Hunter-Saxton system.

Related

• Blow-up phenomena and global existence for a periodic two-component Hunter-Saxton system
• On the Cauchy problem of a periodic 2-component μ-Hunter-Saxton equation
• The Cauchy problem of a periodic 2-component μ-Hunter-Saxton system in Besov spaces
• Global estimates and blow-up criteria for the generalized Hunter-Saxton system
• Blow-up phenomena and global existence for the periodic two-component Dullin-Gottwald-Holm system