Bingham Viscoplastic as a Limit of Non-Newtonian Fluids

A new formulation is proposed for the equations of the Bingham viscoplastic. Global existence of x--periodic solutions is proved. A uniqueness theorem is established in the two-dimensional case. A relation with the G. Duvaut--J. L. Lions variational inequality is discussed, and a result on equivalence is obtained. The question of interaction between fluid-rigid phases is studied when the initial state is rigid. A free-boundary problem that describes two-phase one-dimensional flows is considered.