Well-posedness, blow-up phenomena and analyticity for a two-component higher order Camassa Holm system

作者：Zhou, Shouming^*

来源：Mathematische Nachrichten, 2018, 291(10): 1595-1619.

DOI：10.1002/mana.201600469

• 2HOCH
• analyticity
• Gevrey regularity
• local well-posedness
• wave breaking

In this paper, the local well-posedness for the Cauchy problem of a two-component higher-order Camassa-Holm system (2HOCH) is established in Besov spaces B-p,r(s) x B-p,r(s-2) with 1 <= p,r <= + infinity and s > { 2 + 1/p,5/2 } (and also in Sobolev spaces H-s x Hs-2 = B-2,2(s) x B-2,2(s-2) with s > 5/2), which improves the corresponding results for higher-order Camassa-Holm in [7,24,25], where the Sobolev index s = 3, s > 7/2, s >= 7/2 is required, respectively. Then the precise blow-up mechanism and global existence for the strong solutions of 2HOCH are determined in the lowest Sobolev space H-s x Hs-2 with s > 5/2. Finally, the Gevrey regularity and analyticity of the 2HOCH are presented.

• 出版日期2018-7
• 单位重庆师范大学