{
  "abstract": "We study the Vlasov--Poisson--Boltzmann system on the three-dimensional torus under uniform shear flow. For Maxwell molecules with Grad's angular cutoff and sufficiently small shear rate, we consider perturbations around the spatially homogeneous self-similar profile of the sheared Boltzmann equation. In self-similar variables, we prove the global stability of this profile, including global existence and uniqueness, the exponential decay of nonzero-spatial derivatives in weighted $L^\\infty$ spaces, and the uniform boundedness of the renormalized perturbation. The analysis combines a Caflisch's decomposition, Guo's $L^\\infty$--$L^2$ estimates, macro--micro analysis, and a spectral study of the zero-frequency mode. We further derive a closed zero-frequency system for a renormalized total energy and suitable second-order moments, which yields a precise large-time description of the shear-induced energy growth.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.13356",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhida Chang"
    },
    {
      "name": "Mingying Zhong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ejm11exa6rwvr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.13356",
  "fulltext_url": null,
  "id": "ejm11exa6rwvr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.13356",
  "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",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7203476628",
  "pdf_url": "https://arxiv.org/pdf/2608.13356",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ejm11exa6rwvr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.13356",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.13356"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global Stability and Energy Growth in the Sheared Vlasov--Poisson--Boltzmann System",
  "title_text": "Global Stability and Energy Growth in the Sheared Vlasov--Poisson--Boltzmann System",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/ejm11exa6rwvr",
  "venue": "arXiv",
  "versions": []
}