{
  "id": "1811.03249",
  "version": "v1",
  "published": "2018-11-08T03:39:28.000Z",
  "updated": "2018-11-08T03:39:28.000Z",
  "title": "Global Navier-Stokes flows for non-decaying initial data with slowly decaying oscillation",
  "authors": [
    "Hyunju Kwon",
    "Tai-Peng Tsai"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Consider the Cauchy problem of incompressible Navier-Stokes equations in $\\mathbb{R}^3$ with uniformly locally square integrable initial data. If the square integral of the initial datum on a ball vanishes as the ball goes to infinity, the existence of a time-global weak solution has been known. However, such data do not include constants, and the only known global solutions for non-decaying data are either for perturbations of constants, or when the velocity gradients are in $L^p$ with finite $p$. In this paper, we construct global weak solutions for non-decaying initial data whose local oscillations decay, no matter how slowly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-08T03:39:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D05",
      "35D30"
    ],
    "keywords": [
      "initial datum",
      "non-decaying initial data",
      "global navier-stokes flows",
      "slowly decaying oscillation",
      "square integrable initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}