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

Finite dimensional uniform attractors for the nonautonomous Camassa-Holm equations

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.