{
  "id": "2312.02874",
  "version": "v1",
  "published": "2023-12-05T16:40:53.000Z",
  "updated": "2023-12-05T16:40:53.000Z",
  "title": "Unified theory on V-states structures for active scalar equations",
  "authors": [
    "Taoufik Hmidi",
    "Liutang Xue",
    "Zhilong Xue"
  ],
  "comment": "48 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper revolves around the existence of V-states close to Rankine vortices for active scalar equations with completely monotone kernels. This allows to unify various results on this topic related to geophysical flows. A key ingredient is a new factorization formula for the spectrum using a universal function which is independent of the model. This function admits several interesting properties allowing to track the spectrum distribution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-05T16:40:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "35Q86",
      "76U05"
    ],
    "keywords": [
      "active scalar equations",
      "v-states structures",
      "unified theory",
      "v-states close",
      "rankine vortices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}