{
  "id": "2305.02237",
  "version": "v1",
  "published": "2023-05-03T16:18:21.000Z",
  "updated": "2023-05-03T16:18:21.000Z",
  "title": "Finite time blow-up in higher dimensional two species problem in the Cauchy problem",
  "authors": [
    "Tae Gab Ha",
    "Seyun Kim"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study the blow-up radial solution of fully parabolic system with higher dimensional two species Cauchy problem for some initial condition. In addition, we show that the set of positive radial functions in $L^{1}(\\mathbb{R})\\cap BUC(\\mathbb{R}^{N}) \\times L^{1}(\\mathbb{R})\\cap BUC(\\mathbb{R}^{N}) \\times W^{1,1}(\\mathbb{R}^{N}) \\cap W^{1,\\infty}(\\mathbb{R}^{N})$ has a dense subset composed of positive radial initial data causing blow-up in finite time with respect to topology $L^{p}(\\mathbb{R}^{N}) \\times L^{p}(\\mathbb{R}^{N}) \\times H^{1}(\\mathbb{R}^{N})\\cap W^{1,1}(\\mathbb{R}^{N})$ for $p \\in \\left[1,\\frac{2N}{N+2}\\right)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-03T16:18:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B44",
      "35Q92",
      "92C17"
    ],
    "keywords": [
      "finite time blow-up",
      "cauchy problem",
      "higher dimensional",
      "species problem",
      "radial initial data causing blow-up"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}