Existence and weak-strong uniqueness for Maxwell-Stefan-Cahn-Hilliard systems

Xiaokai Huo, Ansgar Jüngel, Athanasios Tzavaras

Research output: Contribution to journalArticlepeer-review


A Maxwell–Stefan system for fluid mixtures with driving forces depending on Cahn–Hilliard-type chemical potentials is analyzed. The corresponding parabolic crossdiffusion equations contain fourth-order derivatives and are considered in a bounded domain with no-flux boundary conditions. The nonconvex part of the energy is assumed to have a bounded Hessian. The main difficulty of the analysis is the degeneracy of the diffusion matrix, which is overcome by proving the positive definiteness of the matrix on a subspace and using the Bott–Duffin matrix inverse. The global existence of weak solutions and a weak-strong uniqueness property are shown by a careful combination of (relative) energy and entropy estimates, yielding H2 (Ω) bounds for the densities, which cannot be obtained from the energy or entropy inequalities alone.
Original languageEnglish (US)
JournalAccepted by Annales de l'Institut Henri Poincaré C, Analyse non linéaire
StatePublished - Feb 26 2023


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