Open Access Research

Blow-up and local weak solution for a modified two-component Camassa-Holm equations

Lixin Tian* and Minyi Zhu

Author Affiliations

Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, People's Republic of China

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Boundary Value Problems 2012, 2012:52 doi:10.1186/1687-2770-2012-52

Published: 2 May 2012

Abstract

In this article, we establish some blow-up results for a modified two-component Camassa-Holm system in Sobolev spaces. We also obtain the existence of the weak solutions of this system in Hs × Hs-1, s > 5/2.

Keywords:
the modified two-component Camassa-Holm equations; blow up; weak solutions.