{
  "id": "2406.09849",
  "version": "v1",
  "published": "2024-06-14T08:57:12.000Z",
  "updated": "2024-06-14T08:57:12.000Z",
  "title": "Steady Contiguous Vortex-Patch Dipole Solutions of the 2D Incompressible Euler Equation",
  "authors": [
    "De Huang",
    "Jiajun Tong"
  ],
  "comment": "41 pages, 6 figures",
  "categories": [
    "math.AP",
    "physics.flu-dyn"
  ],
  "abstract": "We construct the first steady traveling wave solutions of the 2D incompressible Euler equation that take the form of a contiguous vortex-patch dipole, which can be viewed as the vortex-patch counterpart of the well-known Lamb-Chaplygin dipole. Our construction is based on a novel fixed-point approach that determines the patch boundary as the fixed point of a certain nonlinear map. Smoothness and other properties of the patch boundary are also obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-14T08:57:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q31",
      "35C07",
      "76B47"
    ],
    "keywords": [
      "2d incompressible euler equation",
      "steady contiguous vortex-patch dipole solutions",
      "steady traveling wave solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}