{
  "id": "1409.1648",
  "version": "v1",
  "published": "2014-09-05T02:50:44.000Z",
  "updated": "2014-09-05T02:50:44.000Z",
  "title": "Long time well-posdness of Prandtl system with small and analytic initial data",
  "authors": [
    "Ping Zhang",
    "Zhifei Zhang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we investigate the long time existence and uniqueness of small solution to $d,$ for $d=2,3,$ dimensional Prandtl system with small initial data which is analytic in the horizontal variables. In particular, we prove that $d$ dimensional Prandtl system has a unique solution with the life-span of which is greater than $\\e^{-\\f43}$ if both the initial data and the value on the boundary of the tangential velocity of the outflow are of size $\\e.$ We mention that the tool developed in \\cite{Ch04, CGP} to make the analytical type estimates and the special structure of the nonlinear terms to this system play an essential role in the proof of this result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-05T02:50:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D05"
    ],
    "keywords": [
      "analytic initial data",
      "long time well-posdness",
      "dimensional prandtl system",
      "long time existence",
      "small initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.1648Z"
    }
  }
}