{
  "id": "1603.03211",
  "version": "v1",
  "published": "2016-03-10T10:35:17.000Z",
  "updated": "2016-03-10T10:35:17.000Z",
  "title": "On global solutions to the Navier-Stokes system with large $L^{3,\\infty}$ initial data",
  "authors": [
    "T. Barker",
    "G. Seregin"
  ],
  "comment": "30 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper addresses a question concerning the behaviour of a sequence of global solutions to the Navier-Stokes equations, with the corresponding sequence of smooth initial data being bounded in the (non-energy class) weak Lebesgue space $L^{3,\\infty}$. It is closely related to the question of what would be a reasonable definition of global weak solutions with a non-energy class of initial data, including the aforementioned Lorentz space. This paper can be regarded as an extension of a similar problem regarding the Lebesgue space $L_3$ to the weak Lebesgue space $L^{3,\\infty}$, whose norms are both scale invariant with the respect to the Navier-Stokes scaling.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-10T10:35:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global solutions",
      "navier-stokes system",
      "weak lebesgue space",
      "non-energy class",
      "global weak solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160303211B"
    }
  }
}