{
  "id": "2002.00159",
  "version": "v1",
  "published": "2020-02-01T07:16:14.000Z",
  "updated": "2020-02-01T07:16:14.000Z",
  "title": "Global Weak Solutions to a Cahn-Hilliard-Navier-Stokes System with Chemotaxis and Singular Potential",
  "authors": [
    "Jingning He"
  ],
  "comment": "35 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We analyze a diffuse interface model that describes the dynamics of incompressible two-phase flows with chemotaxis effect. The PDE system couples a Navier-Stokes equation for the fluid velocity, a convective Cahn-Hilliard equation for the phase field variable with an advection-diffusion-reaction equation for the nutrient density. For the system with a singular potential, we prove the existence of global weak solutions in both two and three dimensions. Besides, in the two dimensional case, we establish a continuous dependence result that implies the uniqueness of global weak solutions. The singular potential guarantees that the phase field variable always stays in the physically relevant interval [-1,1] during time evolution. This property enables us to obtain the well-posedness result without any extra assumption on the coefficients that has been made in the previous literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-01T07:16:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A01",
      "35A02",
      "35K35",
      "35Q92",
      "76D05"
    ],
    "keywords": [
      "global weak solutions",
      "cahn-hilliard-navier-stokes system",
      "chemotaxis",
      "phase field variable",
      "diffuse interface model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}