{
  "id": "2406.16365",
  "version": "v1",
  "published": "2024-06-24T07:16:24.000Z",
  "updated": "2024-06-24T07:16:24.000Z",
  "title": "On the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation with inverse-power potential",
  "authors": [
    "JinMyong An",
    "JinMyong Kim",
    "OkByol Kim"
  ],
  "comment": "31 Pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study the Cauchy problem for the inhomogeneous nonlinear Schr\\\"{o}dinger equation with inverse-power potential \\[iu_{t} +\\Delta u-c|x|^{-a}u=\\pm |x|^{-b} |u|^{\\sigma } u,\\;\\;(t,x)\\in \\mathbb R\\times\\mathbb R^{d},\\] where $d\\in \\mathbb N$, $c\\in \\mathbb R$, $a,b>0$ and $\\sigma>0$. First, we establish the local well-posedness in the fractional Sobolev spaces $H^s(\\mathbb R^d)$ with $s\\ge 0$ by using contraction mapping principle based on the Strichartz estimates in Sobolev-Lorentz spaces. Next, the global existence and blow-up of $H^1$-solution are investigated. Our results extend the known results in several directions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-24T07:16:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35A01",
      "35B44"
    ],
    "keywords": [
      "inhomogeneous nonlinear schrödinger equation",
      "cauchy problem",
      "inverse-power potential",
      "fractional sobolev spaces",
      "global existence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}