{
  "id": "2003.03086",
  "version": "v1",
  "published": "2020-03-06T09:01:12.000Z",
  "updated": "2020-03-06T09:01:12.000Z",
  "title": "Decay and Strichartz estimates for dispersive equations in an Aharonov-Bohm field",
  "authors": [
    "Junyong Zhang",
    "Jiqiang Zheng"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove decay and Strichartz estimates for the dispersive equations with an Aharonov-Bohm potential which is a singular and scaling-critical potential. The decay estimates generalize the results of \\cite{DF} and the Strichartz estimates extend the weighted Strichartz estimates for Dirac proved in \\cite{CF} so that we answer the open problem raised in \\cite{CF,CF1}. In addition, the argument provides a new simple proof of $L^1\\to L^\\infty$-decay estimate of Schr\\\"odinger equation shown in \\cite{FFFP1}. The key point of the argument is to develop the distorted Fourier theory based on an observation of the eigenfunction of the Schr\\\"odinger operator with Aharonov-Bohm potential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-06T09:01:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B37",
      "35Q40",
      "35Q41"
    ],
    "keywords": [
      "dispersive equations",
      "aharonov-bohm field",
      "decay estimate",
      "aharonov-bohm potential",
      "strichartz estimates extend"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}