{
  "id": "2002.04057",
  "version": "v1",
  "published": "2020-02-10T19:28:30.000Z",
  "updated": "2020-02-10T19:28:30.000Z",
  "title": "Maximizers for Strichartz Inequalities on the Torus",
  "authors": [
    "Oreoluwa Adekoya",
    "John P. Albert"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the existence of maximizers for a one-parameter family of Strichartz inequalities on the torus. In general maximizing sequences can fail to be precompact in $L^2(\\mathbb T)$, and maximizers can fail to exist. We provide a sufficient condition for precompactness of maximizing sequences (after translation in Fourier space), and verify the existence of maximizers for a range of values of the parameter. Maximizers for the Strichartz inequalities correspond to stable, periodic (in space and time) solutions of a model equation for optical pulses in a dispersion-managed fiber.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-10T19:28:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35B45"
    ],
    "keywords": [
      "maximizers",
      "strichartz inequalities correspond",
      "sufficient condition",
      "general maximizing sequences",
      "fourier space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}