{
  "abstract": "This work investigates rigorously the convergence properties of a spectral semi-Galerkin approximation for three-dimensional inhomogeneous nematic liquid crystal flows. To overcome the analytical barriers posed by the hyperbolic density transport and the pointwise geometric constraint $|d|=1$, we analyze a decoupled scheme that projects only the velocity onto a finite-dimensional space. Assuming uniform local-in-time bounds, we first derive basic error estimates of order $O(\\lambda_{k+1}^{-1})$. Through higher-order $H^3$ estimates, we then prove an convergence rate of $O(\\lambda_{k+1}^{-3/2})$ in the $L^2$ norm. Our results provide a structure-preserving framework for the rigorous analysis of complex non-homogeneous liquid crystal flows.",
  "abstract_shown": true,
  "affiliations": [
    "Univ. de Tarapaca, Arica, Chile"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Lucas Mascarenhas-Silva"
    },
    {
      "affs": [
        0
      ],
      "name": "Marko Antonio Rojas-Medar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a39cy75smtqd7.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": "http://ejde.math.txstate.edu/Volumes/2026/64/abstr.html",
  "id": "a39cy75smtqd7",
  "issns": [
    "1072-6691"
  ],
  "landing_url": "http://ejde.math.txstate.edu/Volumes/2026/64/abstr.html",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QA1-939"
    ]
  ],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-01",
  "publisher": "Texas State University",
  "ris": "https://research.draconitic.com/paper/a39cy75smtqd7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:22Z",
      "native_id": "0a2baace378d4a2f801f99f8d1a0e7e9",
      "source": "doaj",
      "url": "http://ejde.math.txstate.edu/Volumes/2026/64/abstr.html"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "lcc:QA1-939",
      "subfield": "general"
    }
  ],
  "title": "Error estimates for semi-Galerkin approximations of the 3D inhomogeneous nematic liquid crystal flows",
  "title_text": "Error estimates for semi-Galerkin approximations of the 3D inhomogeneous nematic liquid crystal flows",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:44:04Z",
  "url": "https://research.draconitic.com/paper/a39cy75smtqd7",
  "venue": "Electronic Journal of Differential Equations",
  "versions": []
}