{
  "id": "2108.11434",
  "version": "v1",
  "published": "2021-08-25T19:01:53.000Z",
  "updated": "2021-08-25T19:01:53.000Z",
  "title": "Blow-up of non-radial solutions for the $L^2$ critical inhomogeneous NLS equation",
  "authors": [
    "Mykael Cardoso",
    "Luiz Gustavo Farah"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the $L^2$ critical inhomogeneous nonlinear Schr\\\"odinger (INLS) equation in $\\mathbb{R}^N$ $$ i \\partial_t u +\\Delta u +|x|^{-b} |u|^{\\frac{4-2b}{N}}u = 0, $$ where $N\\geq 1$ and $0<b<2$. We prove that if $u_0\\in H^1(\\mathbb{R}^N)$ satisfies $E[u_0]<0$, then the corresponding solution blows-up in finite time. This is in sharp contrast to the classical $L^2$ critical NLS equation where this type of result is only known in the radial case for $N\\geq 2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-25T19:01:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35B44"
    ],
    "keywords": [
      "critical inhomogeneous nls equation",
      "non-radial solutions",
      "corresponding solution blows-up",
      "finite time",
      "sharp contrast"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}