Pullback dynamic behavior for a non-autonomous incompressible non-Newtonian fluid

Abstract

This paper studies the pullback asymptotic behavior of solutions for a non-autonomous incompressible non-Newtonian fluid on 2D bounded domains. We show existence of the pullback exponential attractor introduced by Langa, Miranville and Real [27], moreover, give existence of the global pullback attractor with finite fractal dimension and reveal the relationship between the global pullback attractor and the pullback exponential attractor. These results improve our previous associated results in papers [29, 40] for the non-Newtonian fluid. 2 i,j=1 |e ij (u)| 2 , and µ 0 , µ 1 , α, η are parameters associated to the fluid which generally depend on the temperature and pressure. In this paper we assume that µ 0 , µ 1 , η are positive constants and 0 < α < 1.