On a new diffuse interface model for incompressible two-phase flows with different densities

We discuss different models for a two-phase flow of two immiscible, incompressible fluids in the case when the densities of the fluids are different. In particular we will present a new thermodynamically consistent diffuse interface model and compare it with the known models. 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 briefly discuss its derivation and its sharp interface limits. Moreover, we present a recent result on existence of weak solutions for this model.