{
  "id": "1809.03310",
  "version": "v1",
  "published": "2018-09-10T13:47:23.000Z",
  "updated": "2018-09-10T13:47:23.000Z",
  "title": "Global existence and boundedness in a chemotaxis-Stokes system with slow $p$-Laplacian diffusion",
  "authors": [
    "Weirun Tao",
    "Yuxiang Li"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper deals with a boundary-value problem in three-dimensional smooth bounded convex domains for the coupled chemotaxis-Stokes system with slow $p$-Laplacian diffusion \\begin{equation} \\left\\{ \\begin{aligned} &n_t+u\\cdot\\nabla n=\\nabla\\cdot\\left(|\\nabla n|^{p-2}\\nabla n\\right)-\\nabla\\cdot(n\\nabla c), &x\\in\\Omega,\\ t>0,\\ \\ &c_t+u\\cdot\\nabla c=\\Delta c-nc,&x\\in\\Omega,\\ t>0,\\ \\ &u_t=\\Delta u+\\nabla P+n\\nabla\\phi ,&x\\in\\Omega,\\ t>0,\\ \\ &\\nabla\\cdot u=0, &x\\in\\Omega,\\ t>0,\\ \\ \\end{aligned} \\right. \\end{equation} where $\\phi\\in W^{2,\\infty}(\\Omega)$ is the gravitational potential. It is proved that global bounded weak solutions exist whenever $p>\\frac{23}{11}$ and the initial data $(n_0,c_0,u_0)$ are sufficiently regular satisfying $n_0\\geq 0$ and $c_0\\geq 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-10T13:47:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q92",
      "35K55",
      "35Q35",
      "76S05",
      "92C17"
    ],
    "keywords": [
      "laplacian diffusion",
      "global existence",
      "three-dimensional smooth bounded convex domains",
      "boundedness",
      "global bounded weak solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}