ON THE CAHN-HILLIARD-BRINKMAN SYSTEM WITH SINGULAR POTENTIAL AND NONCONSTANT VISCOSITY

Monica Conti (1) , Andrea Giorgini (1)

1 POLIMI - Politecnico di Milano [Milan]

The Cahn–Hilliard–Brinkman system has been recently proposed as a diffuse interface model for the phase separation of incompressible binary fluids in porous media. It consists of a Brinkman–Darcy equation governing the fluid velocity, nonlin-early coupled with a convective Cahn–Hilliard equation for the relative difference of the fluid concentrations. We prove existence and uniqueness of finite energy solutions in two space dimensions for a class of physically relevant and singular free energy density, in the case of concentration-dependent viscosity. Then, we discuss their regularization properties in finite time and we establish the strict separation property from the pure states.

Mots clés: Diffuse interface models; Cahn–Hilliard equation; Darcy's law; singular po-; strict separation property; 35Q35; 76D27; 76S05

Domaines: Equations aux dérivées partielles [math.AP]

Monica Conti, Andrea Giorgini. ON THE CAHN-HILLIARD-BRINKMAN SYSTEM WITH SINGULAR POTENTIAL AND NONCONSTANT VISCOSITY. 2017. ⟨hal-01559179v1⟩