{
  "id": "1405.7330",
  "version": "v2",
  "published": "2014-05-28T18:42:30.000Z",
  "updated": "2015-02-08T14:59:33.000Z",
  "title": "On nonlinear Schrödinger equations with almost periodic initial data",
  "authors": [
    "Tadahiro Oh"
  ],
  "comment": "18 pages. References updated. To appear in SIAM J. Math. Anal",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the Cauchy problem of nonlinear Schr\\\"odinger equations (NLS) with almost periodic functions as initial data. We first prove that, given a frequency set $\\pmb{\\omega} =\\{\\omega_j\\}_{j = 1}^\\infty$, NLS is local well-posed in the algebra $\\mathcal{A}_{\\pmb{\\omega}}(\\mathbb R)$ of almost periodic functions with absolutely convergent Fourier series. Then, we prove a finite time blowup result for NLS with a nonlinearity $|u|^p$, $p \\in 2\\mathbb{N}$. This elementary argument presents the first instance of finite time blowup solutions to NLS with generic almost periodic initial data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-28T18:42:30.000Z",
      "abstract": "We consider the Cauchy problem of nonlinear Schr\\\"odinger equations (NLS) with almost periodic functions as initial data. We first prove that, given a frequency set $\\pmb{\\omega} =\\{ \\omega_j\\}_{j = 1}^\\infty$, NLS is local well-posed in the algebra $\\mathcal{A}_{\\pmb{\\omega}}(\\mathbb R)$ of almost periodic functions with absolutely convergent Fourier series. Then, we prove a finite time blowup result for NLS with a nonlinearity $|u|^p$, $p \\in 2\\mathbb{N}$. This elementary argument presents the first instance of finite time blowup solutions to NLS with generic almost periodic initial data.",
      "comment": "18 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-08T14:59:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic initial data",
      "nonlinear schrödinger equations",
      "finite time blowup solutions",
      "finite time blowup result",
      "periodic functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.7330O"
    }
  }
}