Abstract and Applied Analysis
Volume 2009 (2009), Article ID 952657, 15 pages
doi:10.1155/2009/952657
Research Article

Finite Dimensional Uniform Attractors for the Nonautonomous Camassa-Holm Equations

Delin Wu

College of Science, China Jiliang University, Hangzhou 310018, China

Received 3 February 2009; Accepted 22 June 2009

Academic Editor: Yong Zhou

Copyright © 2009 Delin 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

We consider the uniform attractors for the three-dimensional nonautonomous Camassa-Holm equations in the periodic box Ω=[0,L]3. Assuming f=f(x,t)∈Lloc2((0,T);D(A−1/2)), we establish the existence of the uniform attractors in D(A1/2) and D(A). The fractal dimension is estimated for the kernel sections of the uniform attractors obtained.