We discuss a diffuse interface 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 Newtonian and non-Newtonian fluids.

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