{
  "id": "1806.01030",
  "version": "v1",
  "published": "2018-06-04T09:49:16.000Z",
  "updated": "2018-06-04T09:49:16.000Z",
  "title": "Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities and Nonlocal Free Energies",
  "authors": [
    "Helmut Abels",
    "Yutaka Terasawa"
  ],
  "comment": "27 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids with different densities in a bounded domain in two and three space dimensions. In contrast to previous works, we study a model with a singular non-local free energy, which controls the $H^{\\alpha/2}$-norm of the volume fraction. We show existence of weak solutions for large times with the aid of an implicit time discretization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-04T09:49:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76T99",
      "35Q30",
      "35Q35",
      "76D03",
      "76D05",
      "76D27",
      "76D45"
    ],
    "keywords": [
      "diffuse interface model",
      "nonlocal free energies",
      "weak solutions",
      "two-phase flows",
      "incompressible fluids"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}