  In this paper we study the existence of weak solutions to an unsteady system
describing the motion of micro-polar electrorheological fluids. The
constitutive relations for the stress tensors belong to the class of
generalized Newtonian fluids. Using the Lipschitz truncation and the solenoidal
Lipschitz truncation we establish the existence of global solutions for shear
exponents $p>6/5$ in three-dimensional domains.
