We consider a phase field model for the flow of two partly miscibleincompressible, viscous fluids of Non-Newtonian (power law) type. In the modelit is assumed that the densities of the fluids are equal. We prove existence ofweak solutions for general initial data and arbitrarily large times with theaid of a parabolic Lipschitz truncation method, which preserves solenoidalvelocity fields and was recently developed by Breit, Diening, and Schwarzacher.
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