Communications in Mathematical Sciences

Volume 14 (2016)

Number 2

On the Camassa–Holm system with one mean zero component

Pages: 517 – 534

DOI: http://dx.doi.org/10.4310/CMS.2016.v14.n2.a9

Authors

Zhengguang Guo (College of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang, China)

Weiming Wang (College of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang, China)

Chongbin Xu (College of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang, China)

Abstract

In this paper, a generalized two-component Camassa–Holm model, closely connected to the shallow water theory, is discussed. This two-component Camassa–Holm system is investigated on the local well-posedness and blow-up phenomena. The present work is mainly concerned with the detailed blow-up criteria where some special classes of initial data are involved. Moreover, as a by-product, the blow-up rate is established.

Keywords

two-component Camassa–Holm system, well-posedness, blow-up criteria

2010 Mathematics Subject Classification

35Q35, 37J35, 37L05, 58E35

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