ABSTRACT
In this paper, we prove an existence result in a two-fluids problem. We consider two fluids of Norton-Hoff type with the same exponent occupying a fixed region D of RN and undergoing the action of time-dependant volume forces /. We assume the fluids are non-miscible and denote a and /? their consistencies. The evolution of this system on a time interval / = [0, 1] is modelized as the solution of the following non-linear transmission problem
a = K\e(u)\P-2e(u) on / x D -div (a) + VP - f on I x D div u(t, •) = 0 on I x D u = 0 on I xdD
dtK + VK-u = Q on I xD ( K(0, •) = a*n + /?(! - xn)
where fi is the subset of D occupied by the fluid of consistency a at the initial time. Our point of view is to look for the solution as an evolution of the initial domain fi (and thus an evolution of the interface between the two fluids).
