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