{
  "id": "2410.21855",
  "version": "v1",
  "published": "2024-10-29T08:29:23.000Z",
  "updated": "2024-10-29T08:29:23.000Z",
  "title": "Quantitative estimates for SPDEs on the full space with transport noise and $L^p$-initial data",
  "authors": [
    "Dejun Luo",
    "Bin Xie",
    "Guohuan Zhao"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "For the stochastic linear transport equation with $L^p$-initial data ($1<p<2$) on the full space $\\mathbb{R}^d$, we provide quantitative estimates, in negative Sobolev norms, between its solutions and that of the deterministic heat equation. Similar results are proved for the stochastic 2D Euler equations with transport noise.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-29T08:29:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "initial data",
      "full space",
      "transport noise",
      "quantitative estimates",
      "stochastic linear transport equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}