{
  "abstract": "In this paper, we study a two-dimensional Poisson--Nernst--Planck--Navier--Stokes system in a periodic channel driven by wall motion and an imposed tangential electric field, with two ionic species that may have unequal diffusivities. At the electroneutral Couette state, a diffusivity-weighted ionic energy combines with the triangular structure of the linearized operator to yield exponential linear stability for fixed \\((A,E_0)\\) and all positive diffusivities. Small-data nonlinear exponential stability is then obtained on a complex interpolation space adapted to the graph domain of the generator by combining analytic-semigroup smoothing with quadratic estimates. For unequal diffusivities, the nonzero streamwise modes of the linearized ionic subsystem satisfy a bounded-channel enhanced-dissipation estimate at rate \\(D_{\\min}^{1/3}|A|^{2/3}\\) under an explicit strong-shear condition. When \\(D_+=D_-\\), a Fourier-mode factorization separates the common Couette advection--diffusion operator from a contractive drift--reaction semigroup, so the same scalar mixing rate is retained without any smallness condition on the electrostatic coupling. We also construct an exact Poisson--Boltzmann/electroosmotic Couette family for prescribed wall potentials. For sufficiently small wall-potential amplitude, its linearized generator is a small graph-domain perturbation of the electroneutral generator, which yields linear and nonlinear exponential stability on the same interpolation scale.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29339",
  "author_total": 2,
  "authors": [
    {
      "name": "J. Pan"
    },
    {
      "name": "L. Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2vxr5sw6ff93z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29339",
  "fulltext_url": null,
  "id": "2vxr5sw6ff93z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29339",
  "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|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7214274733",
  "pdf_url": "https://arxiv.org/pdf/2609.29339",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2vxr5sw6ff93z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29339",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29339"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Stability of electrokinetic Couette states in the Poisson--Nernst--Planck--Navier--Stokes system",
  "title_text": "Stability of electrokinetic Couette states in the Poisson--Nernst--Planck--Navier--Stokes system",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/2vxr5sw6ff93z",
  "venue": "arXiv",
  "versions": []
}