Abstract
We first review results about existence of generalized or weak solutions for Newtonian and power-law type two-phase flows. Then we state a recent result by the authors about existence of weak solutions for diffuse interface model of power-law type two-phase flows and give a sketch of its proof. The latter part is a summary of Abels et al. (Nonlinear Anal Real World Appl 15:149–157, 2014).
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