{
  "abstract": "We consider the Nernst--Planck--Darcy system describing the electrodiffusion of $N$ ionic species with arbitrary valences and different diffusivities, transported by a Darcy flow driven by the electric force, in the whole space $\\mathbb{R}^d$, $d \\ge 3$. We prove the existence of global solutions for initial ionic concentrations that are small in the critical Lebesgue space $L^{d/2}(\\mathbb{R}^d)$. Moreover, we establish uniqueness for initial data in $L^{d+ε}(\\mathbb{R}^d)$ when $3 \\le d \\le 4$ and in $L^{2d-1}(\\mathbb{R}^d)$ when $d \\ge 5$, improving on results in the literature, which require Sobolev regularity of the data. The proofs rely on energy estimates exploiting cancellations of the highest-order nonlinear terms, and on the resulting dissipative structures, which yield an instantaneous gain of regularity used to control the doubly nonlinear velocity term in the uniqueness argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14659",
  "author_total": 2,
  "authors": [
    {
      "name": "Elie Abdo"
    },
    {
      "name": "Christofer Ghazale"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6htwzdb4kn5xa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14659",
  "fulltext_url": null,
  "id": "6htwzdb4kn5xa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14659",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7213249202",
  "pdf_url": "https://arxiv.org/pdf/2609.14659",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6htwzdb4kn5xa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14659",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14659"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On a Multispecies Electrodiffusion Model in Higher-Dimensional Porous Media",
  "title_text": "On a Multispecies Electrodiffusion Model in Higher-Dimensional Porous Media",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/6htwzdb4kn5xa",
  "venue": "arXiv",
  "versions": []
}