Global weak solutions to a compressible Navier--Stokes/Cahn--Hilliard system with singular entropy of mixing

Danica Basarić; Andrea Giorgini

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arXiv · 2506.07835

Global weak solutions to a compressible Navier--Stokes/Cahn--Hilliard system with singular entropy of mixing

Danica Basarić·Andrea Giorgini

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Abstract

We study a Navier-Stokes/Cahn-Hilliard system modeling the evolution of a compressible binary mixture of viscous fluids undergoing phase separation. The novelty of this work is a free energy potential including the physically relevant Flory-Huggins (logarithmic) entropy, as opposed to previous studies in the literature, which only consider regular potentials with polynomial growth. Our main result establishes the existence of global-in-time weak solutions in three-dimensional bounded domains for arbitrarily large initial data. The core contribution is the derivation of new estimates for the chemical potential and the Flory-Huggins entropy arising from a density-dependent Cahn-Hilliard equation under minimal assumptions: non-negative $\gamma$-integrable density with $\gamma>\frac32$. In addition, we prove that the phase variable, which represents the difference of the mass concentrations, takes value within the physical interval $(-1,1)$ almost everywhere on the set where the density is positive.

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Danica Basarić, Andrea Giorgini. 2025-06-09. Global weak solutions to a compressible Navier--Stokes/Cahn--Hilliard system with singular entropy of mixing. https://arxiv.org/abs/2506.07835

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