Pullback exponential attractors for the three dimensional non-autonomous Navier-Stokes equations with nonlinear damping

Fang Li, ,School of Mathematics and Statistics, Xidian University, Xi'an 710126, China, Bo You, ,School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China
2017 Discrete and continuous dynamical systems. Series B  
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 [27], 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