{
  "abstract": "In this paper, we investigate the Cauchy problem for a model system of radiating gas in multi-dimensional space. Firstly, we prove that the model is locally well-posed in Besov spaces $B^s_{p,r}(\\mathbb{R}^d)$ with $s>1+\\frac{d}{p}$ (resp., $s=1+\\frac{d}{p}$, $r=1$), including the endpoint space $B^1_{\\infty,1}(\\mathbb{R}^d)$. Secondly, we show that the data-to-solution map is not uniformly continuous on bounded subsets of these Besov spaces. Moreover, we construct a blow-up scenario and derive two sufficient blow-up conditions, which improve the previous blow-up condition obtained in \\cite{MR3016436}. Finally, we prove that the Cauchy problem is ill-posed in the critical space $B^{1+\\frac{d}{p}}_{p,r}(\\mathbb{R}^d)$ for $1\\leq p\\leq\\infty$ and $r>1$ in the sense of norm inflation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29462",
  "author_total": 4,
  "authors": [
    {
      "name": "Jian Chen"
    },
    {
      "name": "Zhaonan Luo"
    },
    {
      "name": "Yuchen Yang"
    },
    {
      "name": "Zhaoyang Yin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/757c03cw05j1x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29462",
  "fulltext_url": null,
  "id": "757c03cw05j1x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29462",
  "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",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7223222937",
  "pdf_url": "https://arxiv.org/pdf/2610.29462",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/757c03cw05j1x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29462",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29462"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Local well-posedness, blow-up phenomenon and ill-posedness for a model system of the radiating gas",
  "title_text": "Local well-posedness, blow-up phenomenon and ill-posedness for a model system of the radiating gas",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/757c03cw05j1x",
  "venue": "arXiv",
  "versions": []
}