The equations for micropolar Bingham fluid are considered and global existence of a weak solution for pressure driven flows is proved for a one-dimensional boundary-value problem with periodic boundary conditions. In contrast to the classical Bingham fluid, the micropolar Bingham fluid supports local micro-rotations and two types of plug zones. Our approach is different from that of Duvaut-Lions developed for the classical Bingham viscoplastic materials. We do not apply the variational inequality but make use an approximation of the generalized Bingham fluid by a Non-Newtonian fluid with a continuous constitutive law
