Convergence of global attractors of a 2D non-Newtonian system to the global attractor of the 2D Navier-Stokes system

Abstract

This paper discusses the relation between the long-time dynamics of solutions of the two-dimensional (2D) incompressible non-Newtonian fluid system and the 2D Navier-Stokes system. We first show that the solutions of the non-Newtonian fluid system converge to the solutions of the Navier-Stokes system in the energy norm. Then we establish that the global attractors \(\{ \mathcal{A}_ \in ^H \} _{0 < \in \leqslant 1} \) of the non-Newtonian fluid system converge to the global attractor A0H of the Navier-Stokes system as e → 0. We also construct the minimal limit AminH of the global attractors \(\{ \mathcal{A}_ \in ^H \} _{0 < \in \leqslant 1} \) as e → 0 and prove that AminH is a strictly invariant and connected set.