{
  "id": "2006.14251",
  "version": "v1",
  "published": "2020-06-25T08:44:30.000Z",
  "updated": "2020-06-25T08:44:30.000Z",
  "title": "Local Well-Posedness of a Quasi-Incompressible Two-Phase Flow",
  "authors": [
    "Helmut Abels",
    "Josef Weber"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show well-posedness of a diffuse interface model for a two-phase flow of two viscous incompressible fluids with different densities locally in time. The model leads to an inhomogeneous Navier-Stokes/Cahn-Hilliard system with a solenoidal velocity field for the mixture, but a variable density of the fluid mixture in the Navier-Stokes type equation. We prove existence of strong solutions locally in time with the aid of a suitable linearization and a contraction mapping argument. To this end we show maximal $L^2$-regularity for the Stokes part of the linearized system and use maximal $L^p$-regularity for the linearized Cahn-Hilliard system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-25T08:44:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76T99",
      "35Q30",
      "35Q35",
      "35R35",
      "76D05",
      "76D45"
    ],
    "keywords": [
      "quasi-incompressible two-phase flow",
      "local well-posedness",
      "diffuse interface model",
      "solenoidal velocity field",
      "navier-stokes type equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}