{
  "abstract": "We establish the long-time behavior of solutions $U$ to first-order Hamilton-Jacobi equations in the Wasserstein space $\\mathcal{P}_2(\\mathbb T^d)$. For a class of Hamiltonians with quadratic growth, including non-convex ones, we prove that there exist a unique ergodic constant $λ$ and a solution $V$ of the associated ergodic problem such that $U(t,m)-λt$ converges to $V(m)$, uniformly on $\\mathcal{P}_2(\\mathbb T^d)$, as $t\\to+\\infty$. Finally, we provide applications to mean field control problems and zero-sum differential games.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01479",
  "author_total": 2,
  "authors": [
    {
      "name": "Erhan Bayraktar"
    },
    {
      "name": "Antonios Zitridis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/65ck68gnpc5k0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01479",
  "fulltext_url": null,
  "id": "65ck68gnpc5k0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01479",
  "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.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01479",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/65ck68gnpc5k0.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01479",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01479"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Long-time behavior of first-order Hamilton-Jacobi equations in the Wasserstein space",
  "title_text": "Long-time behavior of first-order Hamilton-Jacobi equations in the Wasserstein space",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/65ck68gnpc5k0",
  "venue": "arXiv",
  "versions": []
}