{
  "id": "2003.13143",
  "version": "v1",
  "published": "2020-03-29T21:18:03.000Z",
  "updated": "2020-03-29T21:18:03.000Z",
  "title": "Asymptotic behavior of critical dissipative quasi-geostrophic equation in Fourier space",
  "authors": [
    "Jamel Benameur",
    "Saber Ben Abdallah"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we show the global existence for critical dissipative quasi-geostrophic equations if $\\|\\widehat{\\theta^0}\\|_{L^1}$ is small enough; among others we prove the analyticity of such a solution. If in addition the initial condition verifies $|D|^{-\\delta}\\theta^0\\in L^1(\\mathbb R^2)$ with $0<\\delta<1$, then the solution remains regular and $\\lim_{t\\rightarrow\\infty}t^\\delta\\|\\widehat{\\theta}(t)\\|_{L^1}=0$. Fourier analysis and standard techniques are used.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-29T21:18:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical dissipative quasi-geostrophic equation",
      "asymptotic behavior",
      "fourier space",
      "initial condition verifies",
      "solution remains regular"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}