Finite Dimension Behavior of Navier-Stokes Equations with Linear Damping for Multi-connected Bounded Domains

The paper analysis finite dimension behavior of Navier-Stokes equations with linear damping for multi-connected bounded domains in two dimensions.The existence and uniqueness of solution are proved under suitable boundary conditions.We also prove the existence of global attractor A,the upper bound estimates of global attractor's Hausdorff and Fractal dimensions are also given.