{
  "id": "1811.10504",
  "version": "v1",
  "published": "2018-11-26T16:56:24.000Z",
  "updated": "2018-11-26T16:56:24.000Z",
  "title": "Low regularity solutions for gravity water waves II: The 2D case",
  "authors": [
    "Albert Ai"
  ],
  "comment": "89 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The gravity water waves equations describe the evolution of the surface of an incompressible, irrotational fluid in the presence of gravity. The classical regularity threshold for the well-posedness of this system requires initial velocity field in $H^s$, with $s > \\frac{1}{2} + 1$, and can be obtained by proving standard energy estimates. This threshold was improved by additionally proving Strichartz estimates with loss. In this article, we establish the well-posedness result for $s > \\frac{1}{2} + 1 - \\frac{1}{8}$, corresponding to proving lossless Strichartz estimates. This provides the sharp regularity threshold with respect to the approach of combining Strichartz estimates with energy estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-26T16:56:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "low regularity solutions",
      "2d case",
      "strichartz estimates",
      "gravity water waves equations",
      "energy estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 89,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}