{
  "id": "1711.04486",
  "version": "v1",
  "published": "2017-11-13T09:22:47.000Z",
  "updated": "2017-11-13T09:22:47.000Z",
  "title": "Local energy weak solutions for the Navier-Stokes equations in the half-space",
  "authors": [
    "Yasunori Maekawa",
    "Hideyuki Miura",
    "Christophe Prange"
  ],
  "comment": "59 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The purpose of this paper is to prove the existence of global in time local energy weak solutions to the Navier-Stokes equations in the half-space $\\mathbb R^3_+$. Such solutions are sometimes called Lemari\\'e-Rieusset solutions in the whole space $\\mathbb R^3$. The main tool in our work is an explicit representation formula for the pressure, which is decomposed into a Helmholtz-Leray part and a harmonic part due to the boundary. We also explain how our result enables to reprove the blow-up of the scale-critical $L^3(\\mathbb R^3_+)$ norm obtained by Barker and Seregin for solutions developing a singularity in finite time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-13T09:22:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A01",
      "35B44",
      "35B45",
      "35D30",
      "35G61",
      "35Q30",
      "76D03",
      "76D05"
    ],
    "keywords": [
      "navier-stokes equations",
      "half-space",
      "time local energy weak solutions",
      "explicit representation formula",
      "finite time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 59,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}