  In this paper we study the existence of solutions to a steady system that
describes the motion of a micropolar electrorheological fluid. The constitutive
relations for the stress tensors belong to the class of generalized Newtonian
fluids. The analysis of this particular problem leads naturally to weighted
Sobolev spaces. By deploying the Lipschitz truncation technique, we establish
the existence of solutions without additional assumptions on the electric
field.

Analysis of PDEs