{
  "abstract": "This paper studies the following chemotaxis system with nonlinear diffusion and singular sensitivity \\[ \\begin{cases} u_t = \\nabla \\cdot \\left( (u+a)^{m-1} \\nabla u \\right) - χ\\nabla \\cdot \\left( u \\dfrac{\\nabla v}{v^k} \\right), \\\\[4pt] v_t = Δv - v + u, \\end{cases} \\] in a smoothly bounded domain \\(Ω\\subset \\mathbb{R}^n\\), \\(n \\geq 2\\), subject to no-flux boundary conditions, where \\(χ,k,a,m>0\\). For suitably regular initial data, we prove global existence and uniform-in-time boundedness of classical solutions if one of the following conditions holds: \\[ \\begin{aligned} & n=2,\\quad k\\in(0,\\infty),\\quad m>1;\\\\ & n\\ge 3,\\quad k\\in\\left(0,\\tfrac12\\right),\\quad m>1+\\frac{(1-k)(n-2)}{n};\\\\ & n\\ge 3,\\quad k\\in\\left[\\tfrac12,1\\right),\\quad m>\\frac{3n-2}{2n};\\\\ & n\\ge 3,\\quad k\\in[1,\\infty),\\quad m>\\max\\left\\{1,\\frac{3n-2}{2n+2}\\right\\}. \\end{aligned} \\] The main contribution is the physically relevant three-dimensional case. In particular, for every \\(χ>0\\), \\(a>0\\), \\(m>1\\) and \\(k\\ge 1\\), the system admits a global bounded classical solution. Thus, in dimension three, nonlinear diffusion of porous-medium type removes the smallness restriction on the chemotactic sensitivity $χ$ that earlier results require in the case \\(m=1\\) and \\(k\\geq 1\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39507",
  "author_total": 1,
  "authors": [
    {
      "name": "Minh Le"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/787g64498vsr5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39507",
  "fulltext_url": null,
  "id": "787g64498vsr5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39507",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39507",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/787g64498vsr5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39507",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39507"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Boundedness in a chemotaxis system with nonlinear diffusion and singular sensitivity",
  "title_text": "Boundedness in a chemotaxis system with nonlinear diffusion and singular sensitivity",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/787g64498vsr5",
  "venue": "arXiv",
  "versions": []
}