Abstract
The main purpose of this paper is to study the well-posedness of a diffuse interface model of non-Newtonian two-phase flows in [Formula: see text]. First, we prove the local existence of a unique strong solution provided that the initial velocity and initial concentration of two phases are sufficiently regular. Then, by using the energy estimates and standard continuity argument, we show that there exists a unique global strong solution provided that the initial velocity and initial concentration are sufficiently small.
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