Abstract
In this paper we study the existence of weak solutions to an unsteady system describing the motion of micropolar 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.
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