{
  "id": "1908.10955",
  "version": "v1",
  "published": "2019-08-28T21:46:03.000Z",
  "updated": "2019-08-28T21:46:03.000Z",
  "title": "Finite time blow-up for the nematic liquid crystal flow in dimension two",
  "authors": [
    "Chen-Chih Lai",
    "Fanghua Lin",
    "Changyou Wang",
    "Juncheng Wei",
    "Yifu Zhou"
  ],
  "comment": "48pages; any comment is welcome",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the initial-boundary value problem of a simplified nematic liquid crystal flow in a bounded, smooth domain $\\Omega \\subset \\mathbb R^2$. Given any $k$ distinct points in the domain, we develop a new {\\em inner--outer gluing method} to construct solutions which blow up exactly at those $k$ points as $t$ goes to a finite time $T$. Moreover, we obtain a precise description of the blow-up.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-28T21:46:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite time blow-up",
      "simplified nematic liquid crystal flow",
      "initial-boundary value problem",
      "smooth domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}