Existence of steady solutions for micropolar electrorheological fluid flows

Abstract

In this paper we study the existence of weak solutions to a steady system describing the motion of micropolar electrorheological fluids. The constitutive relations for the stress tensors belong to the class of generalized Newtonian fluids. The analysis of the problem leads naturally to weighted Sobolev spaces. The emphasis of the paper is devoted to the study of the degenerate problem. Using the Lipschitz truncation and the L∞-truncation we derive various lower bounds, depending also on the electric field, ensuring the existence of solutions.