2025/06/09 by Danica Basarić, Basarić, Danica, Andrea Giorgini +1
Materials Science · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.2506.07835
openalex publication_date 2025/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 γ-integrable density with γ>\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.