{
  "id": "2212.14067",
  "version": "v1",
  "published": "2022-12-28T19:05:44.000Z",
  "updated": "2022-12-28T19:05:44.000Z",
  "title": "Low regularity well-posedness of KP-I equations: the three-dimensional case",
  "authors": [
    "Sebastian Herr",
    "Akansha Sanwal",
    "Robert Schippa"
  ],
  "comment": "36 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, low regularity local well-posedness results for the Kadomtsev--Petviashvili--I equation posed in spatial dimension $d =3$ are proved. Periodic, non-periodic and mixed settings as well as generalized dispersion relations are considered. In the weak dispersion regime, these initial value problems show a quasilinear behavior so that bilinear and energy estimates on frequency dependent time scales are used in the analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-28T19:05:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "low regularity well-posedness",
      "three-dimensional case",
      "kp-i equations",
      "low regularity local well-posedness results",
      "frequency dependent time scales"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}