Global attractors, exponential attractors and determining modes for the three dimensional Kelvin-Voigt fluids with "fading memory"

<p style='text-indent:20px;'>The three-dimensional viscoelastic fluid flow equations, arising from the motion of Kelvin-Voigt (Kelvin-Voight) fluids in bounded domains is considered this work. We investigate long-term dynamics such equations with "fading memory" (non-autonomous). first establish existence an absorbing ball appropriate spaces for semigroup defined order one (transformed autonomous coupled system). Then, we prove that asymptotically compact, and hence a global attractor semigroup. provide estimates number determining modes both asymptotic as well trajectories on attractor. Once differentiability respect to initial data established, show has finite Hausdorff fractal dimensions. also exponential associated transformed (equivalent) memory". Finally, Ladyzhenskaya's squeezing property quasi-stable, which implies having dimension.</p>