{
  "abstract": "In this paper, we establish a quantitative finite-time approximation of scattering fields for nonlinear Alfvén waves in three-dimensional ideal incompressible magnetohydrodynamics near a strong constant magnetic background. Using the global weighted estimates, we prove that truncating the scattering profiles at time $T$ introduces an error in both the $L^\\infty$ norm and the $H^{N_*+1}$ norm of order $$ O\\bigl(\\varepsilon^2(R+T)^{-δ}\\bigr), $$ where $\\varepsilon\\in (0,1)$ measures the size of the initial perturbation, $R\\ge100$ is the scale parameter in the weighted energy, $δ\\in(0,2/3)$ is the exponent related to weights, and $N_*+1$ is the Sobolev regularity order assumed for the initial data. The pointwise estimate follows from the decay of the nonlocal pressure along nonlinear characteristics, while the Sobolev estimate combines higher-order weighted pressure bounds with estimates for derivatives of the characteristic flows. Numerical experiments measure pointwise and Sobolev pressure-integral tails to verify the quadratic dependence of the initial perturbation amplitude.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11595",
  "author_total": 2,
  "authors": [
    {
      "name": "Junming Duan"
    },
    {
      "name": "Mengni Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ez2j62p0bc5f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11595",
  "fulltext_url": null,
  "id": "1ez2j62p0bc5f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11595",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7221117713",
  "pdf_url": "https://arxiv.org/pdf/2610.11595",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ez2j62p0bc5f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11595",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11595"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Quantitative finite-time approximation of scattering fields for Alfvén waves in ideal MHD",
  "title_text": "Quantitative finite-time approximation of scattering fields for Alfvén waves in ideal MHD",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/1ez2j62p0bc5f",
  "venue": "arXiv",
  "versions": []
}