Abstract and Applied Analysis
Volume 2012 (2012), Article ID 164876, 17 pages
http://dx.doi.org/10.1155/2012/164876
Research Article

On the Study of Local Solutions for a Generalized Camassa-Holm Equation

Meng Wu

School of Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China

Received 23 May 2012; Revised 30 June 2012; Accepted 18 July 2012

Academic Editor: Yong Hong Wu

Copyright © 2012 Meng Wu. 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 pseudoparabolic regularization technique is employed to study the local well-posedness of strong solutions for a nonlinear dispersive model, which includes the famous Camassa-Holm equation. The local well-posedness is established in the Sobolev space 𝐻 𝑠 ( 𝑅 ) with 𝑠 > 3 / 2 via a limiting procedure.