{
  "id": "2003.08198",
  "version": "v1",
  "published": "2020-03-18T13:10:27.000Z",
  "updated": "2020-03-18T13:10:27.000Z",
  "title": "Advection diffusion equations with Sobolev velocity field",
  "authors": [
    "Elia Bruè",
    "Quoc-Hung Nguyen"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this note we study advection diffusion equations associated to incompressible $W^{1,p}$ velocity fields with $p>2$. We present new estimates on the energy dissipation rate and we discuss applications to the study of upper bounds on the enhancing dissipation rate, lower bounds on the $L^2$ norm of the density, and quantitative vanishing viscosity estimates. The key tools employed in our argument are a propagation of regularity result, coming from the study of transport equations, and a new result connecting the energy dissipation rate to regularity estimates for transport equations. Eventually we provide examples which underline the sharpness of our estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-18T13:10:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A12",
      "35F25",
      "35F10"
    ],
    "keywords": [
      "sobolev velocity field",
      "energy dissipation rate",
      "study advection diffusion equations",
      "transport equations",
      "regularity estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}