{
  "id": "2210.01711",
  "version": "v1",
  "published": "2022-10-04T16:14:35.000Z",
  "updated": "2022-10-04T16:14:35.000Z",
  "title": "The Kuramoto-Sivashinsky Equation",
  "authors": [
    "John C. Baez",
    "Steve Huntsman",
    "Cheyne Weis"
  ],
  "comment": "3 pages, 2 figures",
  "journal": "Notices Amer. Math. Soc. 69 (2022), 1581-1583",
  "categories": [
    "math.AP",
    "math.DS",
    "nlin.CD"
  ],
  "abstract": "The Kuramoto-Sivashinsky equation was introduced as a simple 1-dimensional model of instabilities in flames, but it turned out to mathematically fascinating in its own right. One reason is that this equation is a simple model of Galilean-invariant chaos with an arrow of time. Starting from random initial conditions, manifestly time-asymmetric stripe-like patterns emerge. As we move forward in time, it appears that these stripes are born and merge, but do not die or split. We pose a precise conjecture to this effect, which requires a precise definition of 'stripes'.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-04T16:14:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kuramoto-sivashinsky equation",
      "random initial conditions",
      "manifestly time-asymmetric stripe-like patterns emerge",
      "galilean-invariant chaos",
      "precise definition"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Notices Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}