A Note on the Global Attractor for the Three-Dimensional Horizontally Filtered Navier-Stokes Equations

We consider a Large Eddy Simulation (LES) model for an incompressible Newtonian fluid in a box-shaped domain with periodic boundary conditions on the lateral boundaries and homogeneous Dirichlet conditions on the top and bottom. The model is obtained through the application of an anisotropic horizontal filter, defined as the inverse of the corresponding Helmholtz operator. The existence of global "regular weak solutions" for this model is already known [9]. Here, we study the associated dynamics and we show, with elementary methods, the existence of the global attractor in a suitable phase space. This extends the analysis provided in [17].