{
  "id": "1806.02518",
  "version": "v1",
  "published": "2018-06-07T05:39:44.000Z",
  "updated": "2018-06-07T05:39:44.000Z",
  "title": "Initial-Boundary value problem of the Navier-Stokes equations in the half space with nonhomogeneous data",
  "authors": [
    "Tongkeun Chang",
    "Bum Ja Jin"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper discusses the solvability (global in time) of the initial-boundary value problem of the Navier-stokes equations in the half space when the initial data $ h\\in \\dot{ B}_{q \\sigma}^{\\alpha-\\frac{2}{q}}(\\R_+)$ and the boundary data $ g\\in \\dot{ B}_q^{\\alpha-\\frac{1}{q},\\frac{\\al}{2}-\\frac{1}{2q}}({\\mathbb R}^{n-1}\\times {\\mathbb R}_+) $ with $g_n\\in \\dot B^{\\frac12 \\alpha}_q ({\\mathbb R}_+; \\dot B^{-\\frac1q}_q ({\\mathbb R}^{n-1}))\\cap L^q({\\mathbb R}_+;\\dot{B}^{\\alpha-\\frac{1}{q}}(\\Rn))$, for any $0<\\alpha<2$ and $q =\\frac{n+2}{\\alpha+1}$. Compatibility condition is required for $h$ and $g$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-07T05:39:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "initial-boundary value problem",
      "navier-stokes equations",
      "half space",
      "nonhomogeneous data",
      "paper discusses"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}