{
  "id": "1712.07239",
  "version": "v1",
  "published": "2017-12-19T22:11:12.000Z",
  "updated": "2017-12-19T22:11:12.000Z",
  "title": "Critical points of Strichartz functional",
  "authors": [
    "C. Eugene Wayne",
    "Vadim Zharnitsky"
  ],
  "comment": "36 pages, 6 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study a pair of infinite dimensional dynamical systems naturally associated with the study of minimizing/maximizing functions for the Strichartz inequalities for the Schr\\\"odinger equation. One system is of gradient type and the other one is a Hamiltonian system. For both systems, the corresponding sets of critical points, their stability, and the relation between the two are investigated. By a combination of numerical and analytical methods we argue that the Gaussian is a maximizer in a class of Strichartz inequalities for dimensions one, two and three. The argument reduces to verification of an apparently new combinatorial inequality involving binomial coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-19T22:11:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical points",
      "strichartz functional",
      "strichartz inequalities",
      "infinite dimensional dynamical systems",
      "gradient type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}