Homogeneous incompressible Bingham viscoplastic as a limit of bi-viscosity fluids

In this paper, the existence of a weak solution for homogeneous incompressible Bingham fluid is investigated. The rheology of such a fluid is defined by a yield stress τ _y and a discontinuous stress–strain law. This non-Newtonian fluid behaves like a solid at low stresses and like a non-linear fluid above the yield stress. In this work we propose to build a weak solution for Navier stokes Bingham equations using a bi-viscosity fluid as an approximation, in particular, we proved that the bi-viscosity tensor converges weakly to the Bingham tensor. This choice allowed us to show the existence of solutions for a given data f∈ L^2(0,T;V') .