Global existence and local well-posedness for a three-component Camassa-Holm system with N-peakon solutions

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:259

Article

Luo, Wei¹  Yin, Zhaoyang^1,2 

[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China

[2] Macau Univ Sci & Technol, Fac Informat Technol, Macau, Peoples R China

关键词: A three-component Camassa-Holm system;    Local well-posedness;    Blow-up criteria;    Global existence;    Peakon solutions;   

DOI  :  10.1016/j.jde.2015.02.005

来源: Elsevier

【 摘 要 】

In this paper we mainly investigate the Cauchy problem of a three-component Camassa-Holm system. We first prove the local well-posedness of the system in Besov spaces B-p,r(s) with p, r is an element of [1, infinity], s > max{1/p, 1/2} by using the Littlewood-Paley theory and transport equations theory. Then, we establish two blow-up criteria which along with the conservation laws enable us to study global existence. Moreover, if the initial data satisfies some certain sign conditions, we obtain a global existence result. Finally, we verify that the system possesses peakon solutions. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free