The local well-posedness, blow-up criteria and Gevrey regularity of solutions for a two-component high-order Camassa-Holm system

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• 作者：Lei Zhang^a ; ^{lzhang890701@163.com} ; Xiuting Li^b ; ^{lisy121@163.com}
• 关键词：Local well-posedness ; Besov spaces ; Blow-up ; Gevrey regularity ; Analyticity
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：June 2017
• 年：2017
• 卷：35
• 期：Complete
• 页码：414-440
• 全文大小：779 K
• 卷排序：35

文摘

This paper studies the Cauchy problem for a two-component high-order Camassa–Holm system proposed in Escher and Lyons (2015). First, we investigate the local well-posedness of the system in the Besov spaces Bp,rs×Bp,rs−2 with s>max{3+1p,72,4−1p} and p,r∈[1,∞]p,r∈[1,∞]. Second, by means of the Littlewood–Paley decomposition technique and the conservative property at hand, we derive a blow-up criteria for the strong solution. Finally, we study the Gevrey regularity and analyticity of the solutions to the system in the Gevrey–Sobolev spaces. In particular, we get a lower bound of the lifespan and the continuity of the data-to-solution mapping.