{
  "id": "1712.07821",
  "version": "v1",
  "published": "2017-12-21T08:01:00.000Z",
  "updated": "2017-12-21T08:01:00.000Z",
  "title": "Low regularity solutions for gravity water waves",
  "authors": [
    "Albert Ai"
  ],
  "comment": "52 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove local well-posedness for the gravity water waves equations without surface tension, with initial velocity field in $H^s$, $s > \\frac{d}{2} + 1 - \\mu$, where $\\mu = \\frac{1}{10}$ in the case $d = 1$ and $\\mu = \\frac{1}{5}$ in the case $d \\geq 2$, extending previous results of Alazard-Burq-Zuily. The improvement primarily arises in two areas. First, we perform an improved analysis of the regularity of the change of variables from Eulerian to Lagrangian coordinates. Second, we perform a time-interval length optimization of the localized Strichartz estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-21T08:01:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "low regularity solutions",
      "gravity water waves equations",
      "time-interval length optimization",
      "initial velocity field",
      "local well-posedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}