Geodesic
Finite-dimensionality of 2-D micropolar fluid flow with periodic boundary conditions
Piotr Szopa1
1 Institute of Applied Mathematics and Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland
Applicationes Mathematicae, Tome 34 (2007) no. 3, pp. 309-339.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/am34-3-4
Keywords: paper devoted proving finite dimensionality two dimensional micropolar fluid flow periodic boundary conditions define notions determining modes nodes estimate their number check distribution forces moments through modes influences estimate number determining modes estimate dimension global attractor finally compare results analogous results navier stokes equation

Piotr Szopa 1

1 Institute of Applied Mathematics and Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland 
@article{10_4064_am34_3_4,
     author = {Piotr Szopa},
     title = {Finite-dimensionality of {2-D} micropolar fluid
 flow with periodic boundary conditions},
     journal = {Applicationes Mathematicae},
     pages = {309--339},
     publisher = {mathdoc},
     volume = {34},
     number = {3},
     year = {2007},
     doi = {10.4064/am34-3-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am34-3-4/}
}
TY  - JOUR
AU  - Piotr Szopa
TI  - Finite-dimensionality of 2-D micropolar fluid
 flow with periodic boundary conditions
JO  - Applicationes Mathematicae
PY  - 2007
SP  - 309
EP  - 339
VL  - 34
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/am34-3-4/
DO  - 10.4064/am34-3-4
LA  - en
ID  - 10_4064_am34_3_4
ER  - 
%0 Journal Article
%A Piotr Szopa
%T Finite-dimensionality of 2-D micropolar fluid
 flow with periodic boundary conditions
%J Applicationes Mathematicae
%D 2007
%P 309-339
%V 34
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/am34-3-4/
%R 10.4064/am34-3-4
%G en
%F 10_4064_am34_3_4
Piotr Szopa. Finite-dimensionality of 2-D micropolar fluid
 flow with periodic boundary conditions. Applicationes Mathematicae, Tome 34 (2007) no. 3, pp. 309-339. doi : 10.4064/am34-3-4. http://geodesic.mathdoc.fr/articles/10.4064/am34-3-4/

Cité par Sources :