On a System of Equations of a Non-Newtonian Micropolar Fluid

Abstract

We investigate a problem for a model of a non-Newtonian micropolar fluid coupled system. The problem has been considered in a bounded, smooth domain of ${\mathbb{R}}^3$ with Dirichlet boundary conditions. The operator stress tensor is given by $\tau (e(u))=[(\nu +{\nu }_{0}M(|e(u){|}^2))e(u)]$. To prove the existence of weak solutions we use the method of Faedo-Galerkin and compactness arguments. Uniqueness and periodicity of solutions are also considered.