This paper is concerned with the asymptotic stability of global weak and strong solutions for a 3D incompressible functional Brinkman-Forchheimer equation with delay. Under some appropriate assumptions on the external forces especially the averaged state, the well-posedness of 3D functional Brinkman-Forchheimer flow model and its steady state equation have been obtained rstly, then the asymptotic stability of global solutions also derived via the convergence of trajectories for the corresponding systems.

This paper is concerned with the bounded fractal and Hausdorff dimension of the pullback attractors for 2D non-autonomous incompressible Navier-Stokes equations with constant delay terms. Using the construction of trace formula with two bases for phase spaces of product flow, the upper boundedness of fractal dimension has been achieved.