{
  "abstract": "We develop a Monte Carlo lattice Boltzmann method to compute statistical solutions to the three-dimensional incompressible Navier--Stokes and Euler equations. Entropic space-time adaptive relaxation of the higher order kinetic moments yields stable numerical solutions with decreasing viscosity. We provide a convergence analysis that is conditional on four explicitly stated assumptions regarding the discrete dynamics. Under diffusive scaling, the laws of the discrete ensemble converge along a subsequence to a limit satisfying the Foias--Temam Liouville formulation of the Navier--Stokes equations. Consequently, provided the structure function scaling holds uniformly, the vanishing viscosity limit of these measures satisfies the multi-point statistical Euler hierarchy of Fjordholm, Mishra, and Weber. The limit measures inherit the known weak-strong uniqueness principle on the interval of existence of a strong Euler solution. Under explicit scaling assumptions, a Kuznetsov-type argument yields a fractional 1-Wasserstein convergence rate. We present three-dimensional computations of time-dependent statistical solutions along the inviscid limit of the incompressible Navier--Stokes equations together with convergence measurements in the Wasserstein metric. Numerical experiments on a randomized Taylor--Green vortex with 24-dimensional initial uncertainty recover Kolmogorov's K41 scaling for energy spectra and structure functions, exhibit the failure of pathwise strong convergence, and yield Wasserstein convergence rates of about $0.5$ at the onset of turbulence. Finally, error measurements with respect to spectral hyperviscosity computations indicate that the computed limit measure is independent of the numerical regularization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.23786",
  "author_total": 3,
  "authors": [
    {
      "name": "Johannes L. Grafen"
    },
    {
      "name": "Tobias Rohner"
    },
    {
      "name": "Stephan Simonis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5vng7aafebpb1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.23786",
  "fulltext_url": null,
  "id": "5vng7aafebpb1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.23786",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7204252502",
  "pdf_url": "https://arxiv.org/pdf/2608.23786",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5vng7aafebpb1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2608.23786",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.23786"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Computing statistical Euler limits of the Navier--Stokes equations in three dimensions",
  "title_text": "Computing statistical Euler limits of the Navier--Stokes equations in three dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/5vng7aafebpb1",
  "venue": "arXiv",
  "versions": []
}