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 -truncation method we prove existence of weak solutions for a power-law exponent , d  =  2, 3. [ABSTRACT FROM AUTHOR]