{
  "id": "2409.07867",
  "version": "v1",
  "published": "2024-09-12T09:26:24.000Z",
  "updated": "2024-09-12T09:26:24.000Z",
  "title": "Interpolation scattering for wave equations with singular potentials and singular data",
  "authors": [
    "Tran Thi Ngoc",
    "Pham Truong Xuan"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "In this paper we investigate a construction of scattering for wave-type equations with singular potentials on the whole space $\\mathbb{R}^n$ in a framework of weak-$L^p$ spaces. First, we use an Yamazaki-type estimate for wave groups on Lorentz spaces and fixed point arguments to prove the global well-posedness for wave-type equations on weak-$L^p$ spaces. Then, we provide a corresponding scattering results in such singular framework. Finally, we use also the dispersive estimates to establish the polynomial stability and improve the decay of scattering.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-12T09:26:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular potentials",
      "wave equations",
      "singular data",
      "interpolation scattering",
      "wave-type equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}