{
  "id": "2303.06291",
  "version": "v2",
  "published": "2023-03-11T03:03:42.000Z",
  "updated": "2024-07-16T02:47:43.000Z",
  "title": "Well-posedness and scattering for wave equations on hyperbolic spaces with singular data",
  "authors": [
    "Lucas C. F. Ferreira",
    "Pham Truong Xuan"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.DG",
    "math.FA",
    "math.MP"
  ],
  "abstract": "We consider the wave and Klein-Gordon equations on the real hyperbolic space $\\mathbb{H}^{n}$ ($n \\geq2$) in a framework based on weak-$L^{p}$ spaces. First, we establish dispersive estimates on Lorentz spaces in the context of $\\mathbb{H}^{n}$. Then, employing those estimates, we prove global well-posedness of solutions and an exponential asymptotic stability property. Moreover, we develop a scattering theory and construct wave operators in such singular framework.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-07-16T02:47:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular data",
      "wave equations",
      "well-posedness",
      "exponential asymptotic stability property",
      "real hyperbolic space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}