The three-dimensional Cahn-Hilliard-Brinkman system with unmatched viscosities

Monica Conti (1) , Andrea Giorgini (1)

1 POLIMI - Politecnico di Milano [Milan]

This paper is focused on a diffuse interface model for the motion of binary fluids with different viscosities. The system consists of the Brinkman-Darcy equations governing the fluid velocity, nonlinearly coupled with a convective Cahn-Hilliard equation for the difference of the fluid concentrations. For the three-dimensional Cahn-Hilliard-Brinkman system with free energy density of logarithmic type we prove the well-posedness of weak solutions and we establish the global-in-time existence of strong solutions. Furthermore, we discuss the validity of the separation property from the pure states, which occurs instantaneously in dimension two and asymptotically in dimension three.

Mots clés: Darcy's law; Diffuse interface models; strong solutions; separation property; logarithmic potential

Domaines: Equations aux dérivées partielles [math.AP]

Monica Conti, Andrea Giorgini. The three-dimensional Cahn-Hilliard-Brinkman system with unmatched viscosities. 2018. ⟨hal-01559179v2⟩