Weak solutions for a non-Newtonian diffuse interface model with different densities

We consider weak solutions for a diffuse interface model of two non-Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a nonhomogenouos generalized Navier-Stokes system and a Cahn-Hilliard equation. For the Cahn-Hilliard part a smooth free energy density and a constant, positive mobility is assumed. Using the L-infinity-truncation method we prove existence of weak solutions for a power-law exponent p > 2d+2/d+2, d=2, 3.