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 $\Omega$. Assuming $f=f(x,t)\in L_{\text{loc}}^2$, we establish the existence of the uniform attractor in $L^2(\Omega )$ and $D\left(A^{1/2}\right)$. The fractal dimension is estimated for the kernel sections of the uniform attractors obtained.