{
  "id": "1806.00809",
  "version": "v1",
  "published": "2018-06-03T15:17:58.000Z",
  "updated": "2018-06-03T15:17:58.000Z",
  "title": "Microlocal analysis of forced waves",
  "authors": [
    "Semyon Dyatlov",
    "Maciej Zworski"
  ],
  "comment": "23 pages, 4 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We use radial estimates for pseudodifferential operators to describe long time evolution of solutions to $ i u_t - P u = f $ where $ P $ is a self-adjoint 0th order pseudodifferential operator satisfying hyperbolic dynamical assumptions and where $ f $ is smooth. This is motivated by recent results of Colin de Verdi\\`ere and Saint-Raymond [arXiv:1801.05582] concerning a microlocal model of internal waves in stratified fluids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-03T15:17:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "microlocal analysis",
      "forced waves",
      "satisfying hyperbolic dynamical assumptions",
      "operator satisfying hyperbolic dynamical",
      "self-adjoint 0th order pseudodifferential operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}