{
  "id": "2004.02588",
  "version": "v1",
  "published": "2020-03-23T06:06:55.000Z",
  "updated": "2020-03-23T06:06:55.000Z",
  "title": "On the use of the Riesz transforms to determine the pressure term in the incompressible Navier-Stokes equations on the whole space",
  "authors": [
    "Borys Álvarez-Samaniego",
    "Wilson P. Álvarez-Samaniego",
    "Pedro G. Fernández-Dalgo"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We give some conditions under which the pressure term in the incompressible Navier-Stokes equations on the entire $d$-dimensional Euclidean space is determined by the formula $\\displaystyle \\nabla p = \\nabla \\left(\\sum_{i,j=1}^d \\mathcal{R}_i \\mathcal{R}_j (u_i u_j - F_{i,j}) \\right)$, where $d \\in \\{2, 3\\}$, ${\\textbf{u}} := (u_1, \\ldots, u_d)$ is the fluid velocity, $\\mathbb{F}:= (F_{i,j})_{1\\le i,j\\le d}$ is the forcing tensor, and for all $k \\in \\{1, \\ldots, d\\}$, $\\mathcal{R}_k$ is the $k$-th Riesz transform.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-23T06:06:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D05"
    ],
    "keywords": [
      "incompressible navier-stokes equations",
      "pressure term",
      "dimensional euclidean space",
      "th riesz transform",
      "fluid velocity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}