{
  "id": "1501.05171",
  "version": "v1",
  "published": "2015-01-21T13:56:49.000Z",
  "updated": "2015-01-21T13:56:49.000Z",
  "title": "Global weak solutions for the three-dimensional chemotaxis-Navier-Stokes system with nonlinear diffusion",
  "authors": [
    "Qingshan Zhang",
    "Yuxiang Li"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider an initial-boundary value problem for the incompressible chemotaxis-Navier-Stokes equations generalizing the porous-medium-type diffusion model $ \\quad n_t+u\\cdot\\nabla n=\\Delta n^m-\\nabla\\cdot(n\\chi(c)\\nabla c), $ $ \\quad c_t+u\\cdot\\nabla c=\\Delta c-nf(c), $ $ \\quad u_t+\\kappa(u\\cdot\\nabla)u=\\Delta u+\\nabla P+n\\nabla\\Phi, $ $ \\quad \\nabla\\cdot u=0, $ in a bounded convex domain $\\Omega\\subset\\mathbb{R}^3$. It is proved that if $m\\geq\\frac{2}{3}$, $\\kappa\\in\\mathbb{R}$, $0<\\chi\\in C^2([0,\\infty))$, $0\\leq f\\in C^1([0,\\infty))$ with $f(0)=0$ and $\\Phi\\in W^{1,\\infty}(\\Omega)$, then for sufficiently smooth initial data $(n_0, c_0, u_0)$ the model possesses at least one global weak solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-21T13:56:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global weak solution",
      "three-dimensional chemotaxis-navier-stokes system",
      "nonlinear diffusion",
      "porous-medium-type diffusion model",
      "initial-boundary value problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150105171Z"
    }
  }
}