Wave breaking and global existence for the generalized periodic two-component Hunter-Saxton system

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• 作者：Byungsoo Moon ^{byungsoo.moon@mavs.uta.edu} ; Yue Liu ; ^yliu@uta.edu
• 关键词：35B10 ; 35B65 ; 35Q35 ; 34Q85
• 刊名：Journal of Differential Equations
• 出版年：2012
• 期刊代码：74_00220396
• 类别：mt
• 出版时间：1 July, 2012
• 卷：253
• 期：1
• 页码：319-355
• 文件大小：348 K

摘要

In this paper, we study the wave-breaking phenomena and global existence for the generalized two-component Hunter-Saxton system in the periodic setting. We first establish local well-posedness for the generalized two-component Hunter-Saxton 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. Finally, we give a sufficient condition for global solutions.