Local-in-time existence of strong solutions to a quasi-incompressible Cahn--Hilliard--Navier--Stokes system

We analyze a quasi-incompressible Cahn–Hilliard–Navier–Stokes system (qCHNS) for two-phase flows with unmatched densities. The order parameter is the volume fraction difference of the two fluids, while mass-averaged velocity is adopted. This leads to a quasi-incompressible model where the pressure also enters the equation of the chemical potential. We establish local existence and uniqueness of strong solutions by the Banach fixed point theorem and the maximal regularity theory.