{
  "id": "2303.08679",
  "version": "v1",
  "published": "2023-03-15T15:02:29.000Z",
  "updated": "2023-03-15T15:02:29.000Z",
  "title": "Existence of global weak solutions of inhomogeneous incompressible Navier-Stokes equations with mass diffusion",
  "authors": [
    "Eliott Kacedan",
    "Kohei Soga"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper proves existence of a global weak solution of the inhomogeneous (i.e., non-constant density) incompressible Navier-Stokes system with mass diffusion. The system is well-known as the Kazhikhov-Smagulov model. The major novelty of the paper is to deal with the Kazhikhov-Smagulov model possessing the non-constant viscosity without any simplification of higher order nonlinearity. Any global weak solution is shown to have a long time behavior that is consistent with mixing phenomena of miscible fluids. The results also contain a new compactness method of the Aubin-Lions-Simon type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-15T15:02:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global weak solution",
      "inhomogeneous incompressible navier-stokes equations",
      "mass diffusion",
      "kazhikhov-smagulov model",
      "long time behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}