Finite Dimensional Uniform Attractors for the Nonautonomous Camassa-Holm Equations - Delin Wu (Abstract and Applied Analysis)
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)∈𝐿2loc((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.