In this thesis we study the long term behaviour of two hydrodynamics equations namely the Navier-Stokes ∂tu − ∆u + ∇p + (u · ∇)u = g(x) ∇ · u = 0, and the non-autonomous Brinkmann-Forchheimer equations ∂tu − ∆u + f(u) + ∇p + (u · ∇)u = g(x, t) ∇ · u = 0 f(u) ∼ αu|u| r−1 . Both these equations are used to describe the velocity of uids with the Brinkmann-Forchheimer for a ow through a porous medium. We demonstrate here, that under some mild assumptions importantly r > 3, the existence of a uniform attractor can be established for the nonautonomous Brinkmann-Forchheimer equations as well as the smoothness of the solution. Furthermore, under more restrictive assumptions one can establish the maximal regularity of these solutions. Next we show that r = 3 is a critical case for the forced BrinkmannForchheimer equations (BFEs) and that for small α ≪ 1 in the non-linearity the forced BFEs do not posses well-posedness (uniqueness fails). This nonuniqueness is based on the new construction by M.Vishik [72,73]. Lastly, we again apply this construction of Vishik to the 2D Navier-Stokes equations and show a non-global lower bound on the dimension of the global attractor on the whole space and on bounded domains with Dirichlet boundary conditions