{
  "abstract": "We study distributional solutions of pressureless Euler systems on the line. In particular we show that Lagrangian solutions [7], introduced by Brenier, Gangbo, Savaré and Westdickenberg, and entropy solutions [37], studied by Nguyen and Tudorascu for the Euler–Poisson system, are equivalent. For the Euler–Poisson system this can be seen as a generalization to second-order systems of the equivalence between $$L^2$$ L 2 -gradient flows and entropy solutions for a first-order aggregation equation proved by Bonaschi, Carrillo, Di Francesco and Peletier [4]. The key observation is an equivalence between Oleĭnik’s E-condition for conservation laws and a characterization due to Natile and Savaré of the normal cone for $$L^2$$ L 2 -gradient flows. This new equivalence allows us to define unique solutions after blow-up for classical solutions of the Euler–Poisson system with quadratic confinement due to Carrillo, Choi and Zatorska [14], as well as to describe their asymptotic behavior.",
  "abstract_shown": true,
  "affiliations": [
    "Mathematical Institute, University of Oxford, Oxford, UK",
    "Department of Mathematical Sciences, NTNU–Norwegian University of Science and Technology, Trondheim, Norway",
    "Department of Mathematics and Cybernetics, SINTEF Digital, Oslo, Norway"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "José Antonio Carrillo",
      "orcid": "0000-0001-8819-4660"
    },
    {
      "affs": [
        1,
        2
      ],
      "name": "Sondre Tesdal Galtung",
      "orcid": "0000-0001-8146-5069"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/29cyv7demfb4k.bib",
  "cited_by": 12,
  "doi": "10.1007/s00208-026-03522-5",
  "fulltext_url": null,
  "id": "29cyv7demfb4k",
  "issns": [
    "0025-5831",
    "1432-1807"
  ],
  "landing_url": "https://doi.org/10.1007/s00208-026-03522-5",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
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  "openalex": "W4389599591",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/s00208-026-03522-5.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-24",
  "publisher": "Springer Nature",
  "ris": "https://research.draconitic.com/paper/29cyv7demfb4k.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T13:20:42Z",
      "native_id": "W4389599591",
      "source": "openalex",
      "url": "https://doi.org/10.1007/s00208-026-03522-5"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Geometric Analysis and Curvature Flows",
      "subfield": "general"
    }
  ],
  "title": "Equivalence of entropy solutions and gradient flows for pressureless 1D Euler systems",
  "title_text": "Equivalence of entropy solutions and gradient flows for pressureless 1D Euler systems",
  "type": "peer-reviewed",
  "updated_at": "2026-11-09T13:21:00Z",
  "url": "https://research.draconitic.com/paper/29cyv7demfb4k",
  "venue": "Mathematische Annalen",
  "versions": []
}