Free interface evolution in Norton-Hoff flows with numerical aspects

We deal with free boundaries evolution in visco-plastic flows. The fluid motion is governed by the incompressible Norton-Hoff operator in the non-cylindrical quasi-static case coupled with the time-dependent convection system. The novelty of this work is that we supply the existence result of an interface between two non-miscible fluids by the use of the non-smooth evolution theory. We argue some numerical examples to illustrate our result.