{
  "abstract": "We establish a stability threshold for the 3D Boussinesq equations around Couette flow $(y,0,0)$ with linearly stratified temperature profile $1+y$ on $\\mathbb{T}\\times\\mathbb{R}^2$, with distinct viscosity $κ$ and thermal diffusivity $μ$ and arbitrary Brunt-Väisälä frequency $β>0$. Assume that $μ$ and $κ$ are comparable, and set $ν=\\min\\{κ,μ\\}$. For sufficiently small \\(a_0>0\\) and \\(s\\geq4\\), we prove that if the initial perturbation satisfies $\\|(u_{in},θ_{in})\\|_{H^s}+\\|(u_{0,in},θ_{0,in})\\|_{W^{s,1}}\\lesssimν^{\\frac{2}{3}} |\\lnν|^{-2-2a_0}$, then the corresponding solution exists globally in time. We also establish Strichartz-type estimates for zero mode. Moreover, our estimates further allow for a nonlinear amplification of order $ν^{-1/6}$ in the high-regularity norm of the zero mode of the first component $u^1_0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29916",
  "author_total": 2,
  "authors": [
    {
      "name": "Pengyu Chen"
    },
    {
      "name": "Zeren Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9k29dpd8b44sg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29916",
  "fulltext_url": null,
  "id": "9k29dpd8b44sg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29916",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7214324223",
  "pdf_url": "https://arxiv.org/pdf/2609.29916",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9k29dpd8b44sg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29916",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29916"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The stability threshold for Boussinesq equations around stratified Couette flow with unequal viscosity and thermal diffusivity on $\\mathbb{T}\\times\\mathbb{R}^2$",
  "title_text": "The stability threshold for Boussinesq equations around stratified Couette flow with unequal viscosity and thermal diffusivity on 𝕋×ℝ^2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/9k29dpd8b44sg",
  "venue": "arXiv",
  "versions": []
}