Finite dimensionality of 2-D micropolar fluid flow with periodic boundary conditions

TL;DR

This paper investigates the finite-dimensional behavior of 2-D micropolar fluid flows with periodic boundaries, estimating the number of determining modes, nodes, and the global attractor dimension, and comparing with Navier-Stokes results.

Contribution

It introduces estimates for determining modes, nodes, and attractor dimension specific to 2-D micropolar fluids, extending understanding beyond classical Navier-Stokes models.

Findings

Estimated the number of determining modes and nodes.

Calculated the dimension of the global attractor.

Compared micropolar fluid results with Navier-Stokes equations.

Abstract

This paper is devoted to describe 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 the number of them, we also estimate the dimension of the global attractor. Finally we compare our results with analogous results for Navier-Stokes equation.