{
  "id": "1503.08638",
  "version": "v1",
  "published": "2015-03-30T11:10:39.000Z",
  "updated": "2015-03-30T11:10:39.000Z",
  "title": "Solvability of the Initial-Boundary value problem of the Navier-Stokes equations with rough data",
  "authors": [
    "Tongkeun Chang",
    "Bum Ja Jin"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study the initial and boundary value problem of the Navier-Stokes equations in the half space. We prove the unique existence of weak solution $u\\in L^q(\\R_+\\times (0,T))$ with $\\nabla u\\in L^{\\frac{q}{2}}_{loc}(\\R_+\\times (0,T))$ for a short time interval when the initial data $h\\in {B}_q^{-\\frac{2}{q}}(\\R_+)$ and the boundary data $ g\\in L^q(0,T;B^{-\\frac{1}{q}}_q(\\Rn))+L^q(\\Rn;B^{-\\frac{1}{2q}}_q(0,T)) $ with normal component $g_n\\in L^q(0,T;\\dot{B}^{-\\frac{1}{q}}_q(\\Rn))$, $n+2<q<\\infty$ are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-30T11:10:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "initial-boundary value problem",
      "navier-stokes equations",
      "rough data",
      "solvability",
      "short time interval"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}