{
  "id": "1603.04148",
  "version": "v1",
  "published": "2016-03-14T06:49:27.000Z",
  "updated": "2016-03-14T06:49:27.000Z",
  "title": "The Liouville theorem and the $L^2$ decay of the FENE dumbbell model of polymeric flows",
  "authors": [
    "Luo Wei",
    "Yin Zhaoyang"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we mainly investigate the finite extensible nonlinear elastic (FENE) dumbbell model with dimension $d\\geq2$ in the whole space. We first proved that there is only the trivial solution for the steady-state FENE model under some integrable condition. Our obtained results generalize and cover the classical results to the stationary Navier-Stokes equations. Then, we study about the $L^2$ decay of the co-rotation FENE model. Concretely, the $L^2$ decay rate of the velocity is $(1+t)^{-\\frac{d}{4}}$ when $d\\geq3$, and $\\ln^{-k}{(e+t)}, k\\in \\mathds{N}^{+}$ when $d=2$. This result improves considerably the recent result of \\cite{Schonbek2} by Schonbek. Moreover, the decay of general FENE model has been considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-14T06:49:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fene dumbbell model",
      "liouville theorem",
      "polymeric flows",
      "stationary navier-stokes equations",
      "finite extensible nonlinear elastic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160304148W"
    }
  }
}