{
  "id": "1801.03576",
  "version": "v1",
  "published": "2018-01-10T22:42:24.000Z",
  "updated": "2018-01-10T22:42:24.000Z",
  "title": "Analyticity of dissipative-dispersive systems in higher dimensions",
  "authors": [
    "Charalampos Evripidou",
    "Yiorgos-Sokratis Smyrlis"
  ],
  "comment": "7 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate the analyticity of the attractors of a class of Kuramoto-Sivashinsky type pseudo-differential equations in higher dimensions, which are periodic in all spatial variables and possess a universal attractor. This is done by fine-tuning the techniques used in a previous work of the second author, which are based on an analytic extensibility criterion involving the growth of $\\nabla^n u$, as $n$ tends to infinity (here $u$ is the solution). These techniques can now be utilised in a variety of higher dimensional equations possessing universal attractors, including Topper--Kawahara equation, Frenkel--Indireshkumar equations and their dispersively modified analogs. We prove that the solutions are analytic whenever $\\gamma$, the order of dissipation of the pseudo-differential operator, is higher than one. We believe that this estimate is optimal, based on numerical evidence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-10T22:42:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35Q35"
    ],
    "keywords": [
      "higher dimensions",
      "dissipative-dispersive systems",
      "analyticity",
      "kuramoto-sivashinsky type pseudo-differential equations",
      "dimensional equations possessing universal attractors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}