Special Session 85: Phase-field models and their singular limits

A Cahn-Hilliard-Darcy-Forchheimer surfactant model
Maurizio Grasselli
Politecnico di Milano
Italy
Co-Author(s):    B. Ouyang, A. Poiatti, H. Wu
Abstract:
We present a mathematical model for two-phase flows with surfactants in porous media, combining a Darcy--Forchheimer equation with two Cahn--Hilliard equations involving singular potentials. We show the existence of global weak solutions and that, over time, every solution converges to a single equilibrium. A key point is that this convergence holds at the level of weak solutions, without requiring extra regularity, which distinguishes this result from much of the existing literature. Further related results will also be discussed if time permits.