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 A H0 of the Navier-Stokes system as ε → 0. We also construct the minimal limit A Hmin of the global attractors \(\{ \mathcal{A}_ \in ^H \} _{0 < \in \leqslant 1} \) as ε → 0 and prove that A Hmin is a strictly invariant and connected set.
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Zhao, C., Duan, J. Convergence of global attractors of a 2D non-Newtonian system to the global attractor of the 2D Navier-Stokes system. Sci. China Math. 56, 253–265 (2013). https://doi.org/10.1007/s11425-012-4538-0
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DOI: https://doi.org/10.1007/s11425-012-4538-0
Keywords
- non-Newtonian fluid system
- Navier-Stokes system
- global attractors
- infinite dimensional dynamical systems