Abstract: The Hele-Shaw-Cahn-Hilliard model is one of the most popular
system describing two-phase flows in porous media or Hele-Shaw cell
using the phase-field approach. We will discuss the well-posedness and
long-time behavior of the incompressible Hele-Shaw-Cahn-Hilliard
system in two and three spatial dimensions. We show the convergence of
global weak/strong
solution to equilibrium as time goes to infinity. Stability of the
energy minimizers is also discussed.