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.
From: Andrea Giorgini [view email]
[v1]
Mon, 9 Jun 2025 15:00:38 UTC (28 KB)
[v2]
Thu, 18 Jun 2026 14:08:38 UTC (29 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。