{
  "abstract": "In this paper, we study the long-time behavior of the viscous conservation law equation on the whole real line, subject to a white-in-time force and arbitrarily small damping and viscosity constants. We establish polynomial mixing rates in two settings: (a) a general super-quadratic flux with hyperviscous dissipation, where the growth of the nonlinearity is controlled by the order of hyperviscosity, and the force is sufficiently non-degenerate on a generic L2-basis; and (b) a general quadratic flux with standard second-order dissipation, and the force is non-degenerate on some unconditional basis. Both settings include the classical Burgers-type nonlinearity. The proof is based on an abstract polynomial coupling criterion developed in arXiv:2408.00592 and a Foiaş--Prodi estimate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29824",
  "author_total": 2,
  "authors": [
    {
      "name": "Peng Gao"
    },
    {
      "name": "Liying Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c6gk5e09bpkzr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29824",
  "fulltext_url": null,
  "id": "c6gk5e09bpkzr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29824",
  "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",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7204947339",
  "pdf_url": "https://arxiv.org/pdf/2608.29824",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c6gk5e09bpkzr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2608.29824",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29824"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Polynomial mixing for stochastic viscous conservation law equation on the whole line",
  "title_text": "Polynomial mixing for stochastic viscous conservation law equation on the whole line",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/c6gk5e09bpkzr",
  "venue": "arXiv",
  "versions": []
}