{
  "abstract": "We introduce a cross-product Landau gradient that commutes with Gaussian mollification. For the hard-potential interaction kernels of the form $A(|v-v_*|)\\sim \\langle v-v_*\\rangle^γ|v-v_*|^2$ with $γ\\in(-\\infty,1]$, this construction yields a variational characterisation of the gradient-flow structure of the spatially homogeneous Landau equation. The cross-product gradient induces the same gradient-flow geometry as that introduced by Carrillo, Delgadino, Desvillettes and Wu (2024), while providing a different representation of the Landau gradient. The main advantage of this formulation is that it requires only weighted $L^1$-control. We also discuss a similar variational characterisation for the GENERIC structure of the fuzzy Landau equations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07466",
  "author_total": 2,
  "authors": [
    {
      "name": "Manh Hong Duong"
    },
    {
      "name": "Zihui He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a27qbr3hpmr87.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07466",
  "fulltext_url": null,
  "id": "a27qbr3hpmr87",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07466",
  "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",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7211991887",
  "pdf_url": "https://arxiv.org/pdf/2609.07466",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a27qbr3hpmr87.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07466",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07466"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Gradient flow approach to Landau equation: A cross-product structure",
  "title_text": "Gradient flow approach to Landau equation: A cross-product structure",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/a27qbr3hpmr87",
  "venue": "arXiv",
  "versions": []
}