Journal of Applied Mathematics
Volume 2014, Article ID 410981, 17 pages
http://dx.doi.org/10.1155/2014/410981
The Cauchy Problem for a Dissipative Periodic 2-Component Degasperis-Procesi System
1School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China
2Department of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China
Received 28 March 2014; Accepted 16 June 2014; Published 23 July 2014
Academic Editor: Sazzad Hossien Chowdhury
Copyright © 2014 Sen Ming et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The dissipative periodic 2-component Degasperis-Procesi system is investigated. A local well-posedness for the system in Besov space is established by using the Littlewood-Paley theory and a priori estimates for the solutions of transport equation. The wave-breaking criterions for strong solutions to the system with certain initial data are derived.