{
  "id": "2405.10532",
  "version": "v1",
  "published": "2024-05-17T04:23:58.000Z",
  "updated": "2024-05-17T04:23:58.000Z",
  "title": "Local Rigidity of the Couette Flow for the Stationary Triple-Deck Equations",
  "authors": [
    "Sameer Iyer",
    "Yasunori Maekawa"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The Triple-Deck equations are a classical boundary layer model which describes the asymptotics of a viscous flow near the separation point, and the Couette flow is an exact stationary solution to the Triple-Deck equations. In this paper we prove the local rigidity of the Couette flow in the sense that there are no other stationary solutions near the Couette flow in a scale invariant space. This provides a stark contrast to the well-studied stationary Prandtl counterpart, and in particular offers a first result towards the rigidity question raised by R. E. Meyer in 1983.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-17T04:23:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "couette flow",
      "stationary triple-deck equations",
      "local rigidity",
      "well-studied stationary prandtl counterpart",
      "classical boundary layer model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}