On the existence, uniqueness and regularity of solutions for a class of micropolar fluids with shear dependent viscosities

Abstract

In this paper we consider a model describing the motion of a class of micropolar fluids with shear-dependent viscosities in a smooth domain $\Omega\subset \mathbb{R}^2$. Under the conditions that the external force and vortex viscosity $\mu_r$ are small in a suitable sense, we proved the existence and uniqueness of regularized solutions for the problem by using the iterative method.

Keywords

• existence and uniqueness
• regularity
• shear dependent viscosity
• micropolar fluids