This paper is devoted to proving the finite-dimensionality of a two-dimensional micropolar fluid flow with periodic boundary conditions. We define the notions of determining modes and nodes and estimate their number. We check how the distribution of the forces and moments through modes influences the estimate of the number of determining modes. We also estimate the dimension of the global attractor. Finally, we compare our results with analogous results for the Navier-Stokes equation.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am34-3-4,
author = {Piotr Szopa},
title = {Finite-dimensionality of 2-D micropolar fluid flow with periodic boundary conditions},
journal = {Applicationes Mathematicae},
volume = {34},
year = {2007},
pages = {309-339},
zbl = {1137.35006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am34-3-4}
}
Piotr Szopa. Finite-dimensionality of 2-D micropolar fluid flow with periodic boundary conditions. Applicationes Mathematicae, Tome 34 (2007) pp. 309-339. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am34-3-4/