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math.AP2026
Global Quasi-strong Solutions to the Voigt Regularization of a Diffuse Interface Model for Incompressible Two-phase Flows with Bulk-surface Interaction
Patrik Knopf, Maoyin Lv, Hao Wu
We analyze a thermodynamically consistent diffuse interface model for incompressible two-phase viscous flows with unmatched densities in a smooth bounded domain $Ω\subset\mathbb{R}…
math.AP2026
Global weak solutions to a diffuse-interface model for quasi-incompressible two-phase flows with unmatched densities and singular potential
Mingwen Fei, Xiang Fei, Yadong Liu +1
We study a thermodynamically consistent diffuse-interface model that describes the motion of two macroscopically immiscible, incompressible, and viscous Newtonian fluids with unmat…
math.AP2026
The Cahn--Hilliard--Darcy--Forchheimer system with surfactant: Existence and long-time behavior of global weak solutions
Maurizio Grasselli, Bohan Ouyang, Andrea Poiatti +1
We consider a diffuse-interface model for two-phase incompressible viscous flows with a soluble surfactant in a bounded porous medium. This hydrodynamic system consists of a Darcy-…