{
  "abstract": "We establish global well-posedness and a small-noise large deviation principle for the two-dimensional Dean-Kawasaki equation with Coulomb interaction $\\partial_tρ^\\varepsilon=Δρ^\\varepsilon-\\nabla\\cdot(ρ^\\varepsilon(V*ρ^\\varepsilon))-\\sqrt{\\varepsilon}\\nabla\\cdot(\\sqrt{ρ^\\varepsilon}\\circξ^{K(\\varepsilon)})$, where $V=λ_V(\\cos(α_V)\\nabla G+\\sin(α_V)J\\nabla G)$. Here $λ_V\\geq0$ is the interaction strength, $α_V$ is the interaction angle, $G$ is the mean-zero Green function of $-Δ$ on $\\mathbb{T}^2$, $J$ is rotation by $π/2$, and $ξ^K$ is a finite-mode approximation of space-time white noise. For finite-entropy initial data of mass $M$ satisfying $λ_V\\max\\{\\cos(α_V),0\\}M<8π$, the equation with the exact square-root coefficient is globally pathwise well posed at every finite Fourier cutoff in the class of stochastic kinetic solutions. Following Fehrman and Gess (arXiv:1910.11860), we prove a large deviation principle on $L^1((0,T)\\times\\mathbb{T}^2)$ under the scaling $K(\\varepsilon)\\to\\infty$ and $\\varepsilon K(\\varepsilon)^4\\to0$, with good rate function given by the quadratic control problem for the skeleton equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23730",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiaohao Ji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6r7xca8v6q99p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23730",
  "fulltext_url": null,
  "id": "6r7xca8v6q99p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23730",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7214017189",
  "pdf_url": "https://arxiv.org/pdf/2609.23730",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6r7xca8v6q99p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23730",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23730"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Large Deviations for the Two-Dimensional Dean-Kawasaki Equation with Coulomb Interactions",
  "title_text": "Large Deviations for the Two-Dimensional Dean-Kawasaki Equation with Coulomb Interactions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/6r7xca8v6q99p",
  "venue": "arXiv",
  "versions": []
}