We prove existence of weak solutions for a diffuse interface model for theflow of two viscous incompressible Newtonian fluids in a bounded domain in twoand three space dimensions. In contrast to previous works, we study a new modelrecently developed by Abels, Garcke, and Gr\"un for fluids with differentdensities, which leads to a solenoidal velocity field. The model is given by anon-homogeneous Navier-Stokes system with a modified convective term coupled toa Cahn-Hilliard system. The density of the mixture depends on an orderparameter.
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