{
  "abstract": "A bounded time-dependent drift together with an arbitrarily small real potential can produce double exponential decay of the full spatial $L^2$ norm. We prove matching quantitative two-time lower bounds for energy solutions of $\\partial_tu-Δu=vu+w\\cdot\\nabla u$ on $\\mathbb{R}^n$, for $n\\geq3$, when $w\\in L^\\infty_{t,x}$ and either $v$ is sufficiently small in $L^\\infty_tL^{n/2}_x$ or $v\\in L^\\infty_tL^p_x$ for some $n/2<p\\leq\\infty$, without a smallness assumption. In particular, a nonzero global solution satisfies a double exponential lower bound at large times. This decay scale is optimal for these coefficient classes: In every dimension $n\\geq3$, we construct a real bounded drift, a real potential arbitrarily small in the critical space and in any prescribed subcritical $L^p$ space, and a nonzero real energy solution with double exponential decay. The construction localizes Rowan's torus example by absorbing the localization error.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02685",
  "author_total": 2,
  "authors": [
    {
      "name": "Igor Kukavica"
    },
    {
      "name": "Qi Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2kbxe8fkms45d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02685",
  "fulltext_url": null,
  "id": "2kbxe8fkms45d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02685",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7220402850",
  "pdf_url": "https://arxiv.org/pdf/2610.02685",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2kbxe8fkms45d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02685",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02685"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Quantitative Parabolic Decay With Bounded Drift",
  "title_text": "Quantitative Parabolic Decay With Bounded Drift",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/2kbxe8fkms45d",
  "venue": "arXiv",
  "versions": []
}