{
  "id": "math/0609357",
  "version": "v1",
  "published": "2006-09-13T15:03:52.000Z",
  "updated": "2006-09-13T15:03:52.000Z",
  "title": "Global attractors of evolutionary systems",
  "authors": [
    "Alexey Cheskidov"
  ],
  "comment": "21 pages",
  "categories": [
    "math.DS",
    "math.AP"
  ],
  "abstract": "An abstract framework for studying the asymptotic behavior of a dissipative evolutionary system $\\mathcal{E}$ with respect to weak and strong topologies was introduced in [8] primarily to study the long-time behavior of the 3D Navier-Stokes equations (NSE) for which the existence of a semigroup of solution operators is not known. Each evolutionary system possesses a global attractor in the weak topology, but does not necessarily in the strong topology. In this paper we study the structure of a global attractor for an abstract evolutionary system, focusing on omega-limits and attracting, invariant, and quasi-invariant sets. We obtain weak and strong uniform tracking properties of omega-limits and global attractors. In addition, we discuss a trajectory attractor for an evolutionary system and derive a condition under which the convergence to the trajectory attractor is strong.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-13T15:03:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37L05",
      "76D05"
    ],
    "keywords": [
      "global attractor",
      "trajectory attractor",
      "strong topology",
      "3d navier-stokes equations",
      "evolutionary system possesses"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9357C"
    }
  }
}