{
  "id": "2205.06478",
  "version": "v1",
  "published": "2022-05-13T07:17:23.000Z",
  "updated": "2022-05-13T07:17:23.000Z",
  "title": "Existence and weak-strong uniqueness for Maxwell-Stefan-Cahn-Hilliard systems",
  "authors": [
    "Xiaokai Huo",
    "Ansgar Jüngel",
    "Athanasios E. Tzavaras"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "A Maxwell-Stefan system for fluid mixtures with driving forces depending on Cahn-Hilliard-type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations contain fourth-order derivatives and are considered in a bounded domain with no-flux boundary conditions. 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 $H^2(\\Omega)$ bounds for the densities, which cannot be obtained from the energy or entropy inequalities alone.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-13T07:17:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weak-strong uniqueness",
      "maxwell-stefan-cahn-hilliard systems",
      "cross-diffusion equations contain fourth-order derivatives",
      "parabolic cross-diffusion equations contain fourth-order",
      "corresponding parabolic cross-diffusion equations contain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}