{
  "id": "2102.03473",
  "version": "v1",
  "published": "2021-02-06T01:54:09.000Z",
  "updated": "2021-02-06T01:54:09.000Z",
  "title": "Smooth extensions for inertial manifolds of semilinear parabolic equations",
  "authors": [
    "Anna Kostianko",
    "Sergey Zelik"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The paper is devoted to a comprehensive study of smoothness of inertial manifolds for abstract semilinear parabolic problems. It is well known that in general we cannot expect more than $C^{1,\\varepsilon}$-regularity for such manifolds (for some positive, but small $\\varepsilon$). Nevertheless, as shown in the paper, under the natural assumptions, the obstacles to the existence of a $C^n$-smooth inertial manifold (where $n\\in\\mathbb N$ is any given number) can be removed by increasing the dimension and by modifying properly the nonlinearity outside of the global attractor (or even outside the $C^{1,\\varepsilon}$-smooth IM of a minimal dimension). The proof is strongly based on the Whitney extension theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-06T01:54:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35B42",
      "37D10",
      "37L25"
    ],
    "keywords": [
      "semilinear parabolic equations",
      "smooth extensions",
      "abstract semilinear parabolic problems",
      "smooth inertial manifold",
      "whitney extension theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}