Raum 614

We discuss the existence of generalized solutions of the flow of two immiscible, incompressible, viscous Newtonian and Non-Newtonian fluids like oil and water. In general the interface between both fluids will develop singularities due to coalescence or formation of drops. Therefore a suitable weak formulation of the problem is needed. If surface tension effects are neglected, existence of weak solutions globally in time can be shown, but little is known about the interface between both fluids. If surface tension is present, the energy estimates gives an a priori bound on the (d-1)-dimensional Hausdorff measure of the interface, but the existence of weak solutions is open. This might be due to possible oscillation and concentration effects of the interface related to instabilities of the interface as for example fingering, emulsification or just cancellation of area, when two parts of the interface meet. Nevertheless the existence of so-called varifold solutions, where the interface is modeled by a suitable measure, can be shown.

Dr. Helmut Abels

MPI MIS Leipzig