Existence of weak solutions for a diffuse interface model of non-Newtonian two-phase flows

Abels H, Diening L, Terasawa Y. Existence of weak solutions for a diffuse interface model of non-Newtonian two-phase flows. Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal. 2014;15:149-157.We consider a phase field model for the flow of two partly miscible incompressible, viscous fluids of Non-Newtonian (power law) type. In the model it is assumed that the densities of the fluids are equal. We prove existence of weak solutions for general initial data and arbitrarily large times with the aid of a parabolic Lipschitz truncation method, which preserves solenoidal velocity fields and was recently developed by Breit, Diening, and Schwarzacher