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The main objective of this paper is to study the long-time behavior of solutions for the three dimensional non-autonomous Navier-Stokes equations with nonlinear damping for r > 4. Inspired by the the methods of -trajectories in , we will prove the existence of a finite dimensional pullback attractor and a pullback exponential attractor, which gives another way of considering the long-time behavior of the non-autonomous evolutionary equations.doi:10.3934/dcdsb.2019172 fatcat:p6fweuausbcrfkqqjqltuveu4q