{
  "id": "2403.06554",
  "version": "v1",
  "published": "2024-03-11T09:57:56.000Z",
  "updated": "2024-03-11T09:57:56.000Z",
  "title": "Unconditional deep-water limit of the intermediate long wave equation in low-regularity",
  "authors": [
    "Justin Forlano",
    "Guopeng Li",
    "Tengfei Zhao"
  ],
  "comment": "27 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we establish the unconditional deep-water limit of the intermediate long wave equation (ILW) to the Benjamin-Ono equation (BO) in low-regularity Sobolev spaces on both the real line and the circle. Our main tool is new unconditional uniqueness results for ILW in $H^s$ when $s_0<s\\leq \\frac 14$ on the line and $s_0<s< \\frac 12$ on the circle, where $s_0 = 3-\\sqrt{33/4}\\approx 0.1277$. Here, we adapt the strategy of Mo\\c{s}incat-Pilod (2023) for BO to the setting of ILW by viewing ILW as a perturbation of BO and making use of the smoothing property of the perturbation term.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-11T09:57:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q53",
      "35A02",
      "76B55"
    ],
    "keywords": [
      "intermediate long wave equation",
      "unconditional deep-water limit",
      "low-regularity sobolev spaces",
      "unconditional uniqueness results",
      "benjamin-ono equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}