Existence and upper semicontinuity of attractors for a class of non-Newtonian micropolar fluids

M. M. Freitas (), G. M. Araújo (), F. D. M. Bezerra () and M. A. F. Araújo ()
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M. M. Freitas: Federal University of Pará
G. M. Araújo: Federal University of Pará
F. D. M. Bezerra: Universidade Federal da Paraíba
M. A. F. Araújo: Universidade Federal do Maranhão

Partial Differential Equations and Applications, 2021, vol. 2, issue 5, 1-24

Abstract: Abstract In this paper we study the long time behavior of the two-dimensional flow for a class of non-Newtonian micropolar fluids in bounded smooth domains, in the sense of compact global attractors. The energy equation approach is used to prove the existence and upper semicontinuity of global attractors in the natural phase space. We also show the finiteness of the fractal dimension of these attractors using the method of short trajectories developed by Málek and Ne $${\check{\mathrm{c}}}$$ c ˇ as (J Differ Equ 127:498–518, 1996).

Keywords: Fractal dimension; Global attractor; Non-Newtonian micropolar fluid; Upper semicontinuity; Primary 35B40; 35B41; Secondary 35Q30; 76D03 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-021-00117-4

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