{
  "id": "2103.05388",
  "version": "v1",
  "published": "2021-03-09T12:14:31.000Z",
  "updated": "2021-03-09T12:14:31.000Z",
  "title": "Global weak solution of 3D-NSE with exponential damping",
  "authors": [
    "Jamel Benameur"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove the global existence of incompressible Navier-Stokes equations with damping $\\alpha (e^{\\beta |u|^2}-1)u$, where we use Friedrich method and some new tools. The delicate problem in the construction of a global solution, is the passage to the limit in exponential nonlinear term. To solve this problem, we use a polynomial approximation of the damping part and a new type of interpolation between $L^\\infty(\\mathbb{R}^+,L^2(\\mathbb{R}^3))$ and the space of functions $f$ such that $(e^{\\beta|f|^2}-1)|f|^2\\in L^1(\\mathbb{R}^3)$. Fourier analysis and standard techniques are used.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-09T12:14:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76N10",
      "G.1.8"
    ],
    "keywords": [
      "global weak solution",
      "exponential damping",
      "exponential nonlinear term",
      "global existence",
      "fourier analysis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}