| Abstract: |
| A nonlocal Cahn-Hilliard-Darcy system for an incompressible mixture of two fluids consists of a convective nonlocal Cahn-Hilliard equation coupled with a Darcy`s law through the Korteweg force. We will discuss some recent results that have been proven for such system, focusing on the case where the mixing entropy density is of Boltzmann-Gibbs type, the kinematic viscosity depends on the order parameter, and the mobility is degenerate at the pure phases. The main issues will be the existence of different types of solutions, their regularization properties, and the longtime behavior of the associated dynamical system. |
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