{
  "id": "math/0608428",
  "version": "v2",
  "published": "2006-08-16T20:02:55.000Z",
  "updated": "2006-10-12T01:58:33.000Z",
  "title": "Geometry and a priori estimates for free boundary problems of the Euler's equation",
  "authors": [
    "Jalal Shatah",
    "Chongchun Zeng"
  ],
  "comment": "33 pages, submitted, added references",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this paper we derive estimates to the free boundary problem for the Euler equation with surface tension, and without surface tension provided the Rayleigh-Taylor sign condition holds. We prove that as the surface tension tends to zero, when the Rayleigh-Taylor condition is satisfied, solutions converge to the Euler flow with zero surface tension.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-10-12T01:58:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free boundary problem",
      "eulers equation",
      "priori estimates",
      "rayleigh-taylor sign condition holds",
      "zero surface tension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8428S"
    }
  }
}