{
  "id": "2006.15663",
  "version": "v1",
  "published": "2020-06-28T17:46:38.000Z",
  "updated": "2020-06-28T17:46:38.000Z",
  "title": "Inertial manifolds via spatial averaging revisited",
  "authors": [
    "Anna Kostianko",
    "Xinhua Li",
    "Chunyou Sun",
    "Sergey Zelik"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The paper gives a comprehensive study of inertial manifolds for semilinear parabolic equations and their smoothness using the spatial averaging method suggested by G. Sell and J. Mallet-Paret. We present a universal approach which covers the most part of known results obtained via this method as well as gives a number of new ones. Among our applications are reaction-diffusion equations, various types of generalized Cahn-Hilliard equations, including fractional and 6th order Cahn-Hilliard equations and several classes of modified Navier-Stokes equations including the Leray-$\\alpha$ regularization, hyperviscous regularization and their combinations. All of the results are obtained in 3D case with periodic boundary conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-28T17:46:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B33",
      "35B40",
      "35B42",
      "35Q30",
      "76F20"
    ],
    "keywords": [
      "inertial manifolds",
      "6th order cahn-hilliard equations",
      "periodic boundary conditions",
      "semilinear parabolic equations",
      "reaction-diffusion equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}