Global weak solutions exist for the quasi-incompressible Navier-Stokes/Cahn-Hilliard system with unmatched densities, singular potential, and mass-averaged velocity on the 3-torus.
Abels, Existence of weak solutions for a diffuse interface model for viscous, incompressible fluids with general densities, Comm
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Global weak solutions to a diffuse-interface model for quasi-incompressible two-phase flows with unmatched densities and singular potential
Global weak solutions exist for the quasi-incompressible Navier-Stokes/Cahn-Hilliard system with unmatched densities, singular potential, and mass-averaged velocity on the 3-torus.