Abstract
S: On a phase-field model for two-phase flows of viscous incompressible fluids with degenerate mobility Helmut Abels University of Regensburg, Faculty for Mathematics 93040 Regensburg, Germany HELMUT.ABELS@MATHEMATIK.UNI-REGENSBURG.DE We discuss a recent model for the two-phase flow of two immiscible, incompressible fluids in the case when the densities of the fluids are different. Such models were introduced to describe the flow when singularities in the interface, which separates the fluids, (droplet formation/coalescence) occur. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed. We will present recent results on existence of weak solutions for this model in the case of degenerate and non-degenerate mobility. Here the case of degenerate mobility is of special interest since there is no diffusion in the pure phases and the effect of Ostwald ripening does not occur for the sharp interface limit. This is a joint-work with Harald Garcke and Daniel Depner from Regensburg.
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