{
  "id": "1809.09787",
  "version": "v1",
  "published": "2018-09-26T02:50:51.000Z",
  "updated": "2018-09-26T02:50:51.000Z",
  "title": "Global Attractor For Weakly Damped, Forced Mkdv Equation Below Energy Space",
  "authors": [
    "Prashant Goyal"
  ],
  "comment": "34 pages. Submitted on December 15, 2017",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove the existence of the global attractor in $ \\dot H^s$, $s > 11/12$ for the weakly damped and forced mKdV on the one dimensional torus. The existence of global attractor below the energy space has not been known, though the global well-posedness below the energy space is established. We directly apply the I-method to the damped and forced mKdV, because the Miura transformation does not work for the mKdV with damping and forcing terms. We need to make a close investigation into the trilinear estimates involving resonant frequencies, which are different from the bilinear estimates corresponding to the KdV.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-26T02:50:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global attractor",
      "energy space",
      "forced mkdv equation",
      "dimensional torus",
      "global well-posedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}