{
  "abstract": "We consider Dirichlet parabolic systems with measurable, real skew-symmetric zero-order potentials on bounded Lipschitz domains in three dimensions. Although skew-symmetry formally removes the potential from the energy balance, singular coefficients may leave the product $CU$ merely integrable, so testing the equation with the solution is not justified. We overcome this obstruction through bounded-gradient entropy identities and stable approximation. For $C\\in L^r(0,T;L^q(Ω;\\mathbb R^{m\\times m}))$ with $1\\le r\\le\\infty$, $6/5\\le q\\le\\infty$, and $2/r+3/q\\le7/2$, we establish existence and uniqueness in the full energy--distributional class, exact energy equality at every pair of times, Euclidean-vector $L^1$ contraction, and strong convergence of both solutions and coefficient--solution products under strong coefficient approximation. We compare a vectorial entropy proof with a derivation by scalar entropies and spherical averaging, and explain the narrower roles of temporal regularization, convex invariance, and adjoint transposition. An application to diffusion--precession gives quantitative stability under $L^1$ perturbations of prescribed magnetic fields for bounded initial data, including singular fields outside the main mixed-norm range.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26333",
  "author_total": 1,
  "authors": [
    {
      "name": "Francisco Javier Fernández Fernández"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7ckzhjm84dvq0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26333",
  "fulltext_url": null,
  "id": "7ckzhjm84dvq0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26333",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7223029714",
  "pdf_url": "https://arxiv.org/pdf/2610.26333",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7ckzhjm84dvq0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26333",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26333"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Energy Equality, Vectorial $L^1$ Contraction, and Mixed-Norm Stability for Parabolic Systems with Rough Skew-Symmetric Potentials",
  "title_text": "Energy Equality, Vectorial L^1 Contraction, and Mixed-Norm Stability for Parabolic Systems with Rough Skew-Symmetric Potentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/7ckzhjm84dvq0",
  "venue": "arXiv",
  "versions": []
}