{
  "id": "1604.04083",
  "version": "v1",
  "published": "2016-04-14T09:11:38.000Z",
  "updated": "2016-04-14T09:11:38.000Z",
  "title": "The uniform time of existence of the smooth solution for 3D Euler-$α$ equations with Dirichlet boundary conditions",
  "authors": [
    "Aibin Zang"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "After reformulate the incompressible Euler-$\\alpha$ equations in 3D smooth domain with Drichlet data, we obtain the unique classical solutions to Euler-$\\alpha$ equations exist in uniform time interval independent of $\\alpha$. We also show the solution of the Euler-$\\alpha$ converge to the corresponding solution of Euler equation in $L^2$ in space, uniformly in time. In the sequel, it follows that the $H^s$ $(s>\\frac{n}{2}+1)$ solutions of Euler-$\\alpha$ equations exist in any fixed sub-interval of the maximum existent interval for the Euler equations provided that initial is regular enough and $\\alpha$ is small sufficiently.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-14T09:11:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirichlet boundary conditions",
      "smooth solution",
      "uniform time interval independent",
      "euler equation",
      "3d smooth domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160404083Z"
    }
  }
}