Flow of a Bingham Fluid in Contact with a Newtonian Fluid

We study the problem modeling the flow of a Bingham fluid in contact with a newtonian fluid, playing the role of lubricant. This is a free boundary problem coupled by means of diffraction conditions with a boundary value problem of parabolic type. We examine the steady state solutions, the evolutive case with particular regard for the asymptotic behaviour of the solution, and a regularized model related to the appearance of a new rigid zone