The Long Time Behaviors of Non-autonomous Navier-Stokes Equations with Linear Dampness on the Whole R2 Space

Abstract

In this paper, the long time behaviors of non-autonomous Navier-Stokes equations with linear dampness on the whole R² space are considered. The existence of uniform attractor is proved when the external force terms satisfy suitable conditions. Moreover, the upper bounds of the uniform attractor's Hausdorff and Fractal dimensions are obtained.