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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 693010, 21 pages
http://dx.doi.org/10.1155/2012/693010
Research Article

The Space Global Weak Solutions to the Weakly Dissipative Camassa-Holm Equation

Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China

Received 3 August 2012; Accepted 21 September 2012

Academic Editor: Yong H. Wu

Copyright © 2012 Zhaowei Sheng 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 existence of global weak solutions to the Cauchy problem for a generalized Camassa-Holm equation with a dissipative term is investigated in the space × ; provided that its initial value belongs to the space . A one-sided super bound estimate and a space-time higher-norm estimate on the first-order derivatives of the solution with respect to the space variable are derived.