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

Monica Conti 1 Andrea Giorgini 1
1 Dipartimento di Matematica, Politecnico di Milano
Dipartimento di Matematica "F. Brioschi"
Abstract : 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.
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Monica Conti, Andrea Giorgini. The three-dimensional Cahn-Hilliard-Brinkman system with unmatched viscosities. 2018. ⟨hal-01559179v2⟩

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