{
  "abstract": "In this paper, we are concerned with the fine properties of entropy solutions of the Cauchy problem for the one-dimensional pressureless Euler system, wherein the initial density $ρ_0$ is a locally finite Radon measure and the initial velocity $u_0\\in L^\\infty_{ρ_0}$. We employ the solution formula introduced by [F.M. Huang and Z. Wang, Comm. Math. Phys. 222(1) (2001), 117--146.] for this Cauchy problem to analyze the entropy solutions and obtain various new fine properties of entropy solutions; these can be summarized in four aspects: (i) Characteristics and initial waves for the Cauchy problem; (ii) Fine local structures of entropy solutions; (iii) Divides and global structures of entropy solutions; (iv) Invariants and asymptotic behaviors of entropy solutions including the asymptotic profile and the corresponding decay rates. Through these results (i)-(iv), we establish the global dynamic patterns of entropy solutions of the Cauchy problem for the $1$-D pressureless Euler system with general initial data $ρ_0$ being locally finite Radon measures and $u_0\\in L^\\infty_{ρ_0}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05948",
  "author_total": 4,
  "authors": [
    {
      "name": "Gaowei Cao"
    },
    {
      "name": "Kai Hu"
    },
    {
      "name": "Feimin Huang"
    },
    {
      "name": "Guirong Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/98xmg8ff6qdez.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05948",
  "fulltext_url": null,
  "id": "98xmg8ff6qdez",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05948",
  "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",
      "2206|Computational Fluid Dynamics and Aerodynamics"
    ]
  ],
  "openalex": "W7212085634",
  "pdf_url": "https://arxiv.org/pdf/2609.05948",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/98xmg8ff6qdez.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05948",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05948"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global Dynamic Patterns of Entropy Solutions for One-dimensional Pressureless Euler System",
  "title_text": "Global Dynamic Patterns of Entropy Solutions for One-dimensional Pressureless Euler System",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/98xmg8ff6qdez",
  "venue": "arXiv",
  "versions": []
}