{
  "id": "2407.14941",
  "version": "v1",
  "published": "2024-07-20T17:29:21.000Z",
  "updated": "2024-07-20T17:29:21.000Z",
  "title": "Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Local Well-Posedness",
  "authors": [
    "Helmut Abels",
    "Harald Garcke",
    "Andrea Poiatti"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "A Cahn-Hilliard-Navier-Stokes system for two-phase flow on an evolving surface with non-matched densities is derived using methods from rational thermodynamics. For a Cahn-Hilliard energy with a singular (logarithmic) potential short time well-posedness of strong solutions together with a separation property is shown, under the assumption of a priori prescribed surface evolution. The problem is reformulated with the help of a pullback to the initial surface. Then a suitable linearization and a contraction mapping argument for the pullback system are used. In order to deal with the linearized system, it is necessary to show maximal $L^2$-regularity for the surface Stokes operator in the case of variable viscosity and to obtain maximal $L^p$-regularity for the linearized Cahn-Hilliard system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-20T17:29:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D05",
      "35D35",
      "35Q35",
      "76T06"
    ],
    "keywords": [
      "diffuse interface model",
      "two-phase flow",
      "evolving surface",
      "local well-posedness",
      "potential short time well-posedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}