{
  "abstract": "This paper proves generic structural stability for Riemann solutions to $n \\times n$ systems of hyperbolic conservation laws in one spatial dimension. Under assumptions of strict hyperbolicity, genuine nonlinearity, and a regular manifold hypothesis on the Rankine-Hugoniot map, we show that for almost every pair of left and right states, any $n$-wave Riemann solution consisting of Lax-admissible shocks and rarefactions is structurally stable under perturbations of the left state, the right state, and the flux function in the $C^2$ topology. The central new idea is sequential transversality, which chains the $n$ waves through intermediate states and transports their tangent contributions to a common reference point via pushforward maps, reducing the structural stability condition to the invertibility of an $n \\times n$ transversality matrix. We apply the results to the $p$-system, polydisperse particle-laden thin films, and machine-learned flux approximations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28714",
  "author_total": 2,
  "authors": [
    {
      "name": "Hong Kiat Tan"
    },
    {
      "name": "Andrea L. Bertozzi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/44jdj7ny9981w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28714",
  "fulltext_url": null,
  "id": "44jdj7ny9981w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28714",
  "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.DG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2206|Computational Fluid Dynamics and Aerodynamics"
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  "openalex": "W7214335310",
  "pdf_url": "https://arxiv.org/pdf/2609.28714",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/44jdj7ny9981w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28714",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28714"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Generic Structural Stability for Riemann Solutions to $n \\times n$ Systems of Hyperbolic Conservation Laws",
  "title_text": "Generic Structural Stability for Riemann Solutions to n × n Systems of Hyperbolic Conservation Laws",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/44jdj7ny9981w",
  "venue": "arXiv",
  "versions": []
}