Wave breaking and global existence for a weakly dissipative generalized two-component μ-Hunter–Saxton system. (June 2015)

• Record Type: Journal Article
• Authors: Wang, Feng; Li, Fengquan; Chen, Qiaoling
• Is Part Of: Nonlinear analysis. Volume 23(2015)
• Page Start: 61
• Page End: 77
• Publication Date: 2015-06
• Subjects: Generalized two-component μ-Hunter–Saxton system -- Weakly dissipative -- Wave breaking; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2014.11.007
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we study the wave-breaking phenomena and global existence for a weakly dissipative generalized two-component μ -Hunter–Saxton system in the periodic setting. We first establish local well-posedness for the generalized system. We obtain a wave-breaking criterion for solutions and results of wave-breaking solutions with certain initial profiles. We also determine the exact blow-up rate of strong solutions and present a lower bound of the lifespan. Finally, we give a sufficient condition for global solutions.