  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 $\tau_y$ 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.
