The Finite-Dimensional Uniform Attractors for the Nonautonomous g-Navier-Stokes Equations

Abstract

We consider the uniform attractors for the two dimensional nonautonomous g-Navier-Stokes equations in bounded domain Ω. Assuming 𝑓=𝑓(𝑥,𝑡)∈𝐿2loc, we establish the existence of the uniform attractor in 𝐿2(Ω) and 𝐷(𝐴1/2). The fractal dimension is estimated for the kernel sections of the uniform attractors obtained.