{
  "id": "2006.12342",
  "version": "v1",
  "published": "2020-06-22T15:35:37.000Z",
  "updated": "2020-06-22T15:35:37.000Z",
  "title": "On the explicit solutions of separation of variables type for the incompressible 2D Euler equations",
  "authors": [
    "Tomi Saleva",
    "Jukka Tuomela"
  ],
  "comment": "17 pages, 0 figures, submitted to The Journal of Mathematical Fluid Mechanics",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study explicit solutions to the 2 dimensional Euler equations in the Lagrangian framework. All known solutions have been of the separation of variables type, where time and space dependence are treated separately. The first such solutions were known already in the 19th century. We show that all the solutions known previously belong to two families of solutions and introduce three new families of solutions. It seems likely that these are all the solutions that are of the separation of variables type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-22T15:35:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q31",
      "35A09",
      "35A24",
      "76B99"
    ],
    "keywords": [
      "incompressible 2d euler equations",
      "variables type",
      "separation",
      "study explicit solutions",
      "dimensional euler equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}