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| Format: | Recurso digital |
| Sprache: | Englisch |
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Zenodo
2026
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| Online-Zugang: | https://doi.org/10.5281/zenodo.19640181 |
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| _version_ | 1866901261036552192 |
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| author | Barnes, Isaac Yaw |
| author_facet | Barnes, Isaac Yaw |
| contents | <p>I am writing to share a preprint that presents the first <br>systematic numerical measurement of vortex-stretching <br>alignment geometry across spatial dimensions n=2,3,5,10 <br>in the Navier-Stokes equations.</p> <p>The central finding is a viscosity-independent geometric <br>floor in θ_min — the minimum alignment angle between the <br>vorticity tensor and strain-vorticity interaction tensor — <br>that is specific to each dimension. In 3D this floor sits <br>at approximately 48°, is stable across ν=0.001 to 0.0001, <br>and is spatially pinned following a snap event at t*≈1.15.</p> <p>The paper states a precise conjecture: ∃ δ(n)>0 such that <br>θ_min(t) ≥ δ(n) for all smooth solutions. For n=3, proving <br>this conjecture would resolve the Millennium Problem.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19640181 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Dimensional Dependence of Vortex-Stretching Alignment in n-Dimensional Navier-Stokes Equations: Numerical Evidence for a Viscosity-Independent Geometric Floor and a Descent Strategy toward the Millennium Problem Barnes, Isaac Yaw Analysis of PDEs Mathematics <p>I am writing to share a preprint that presents the first <br>systematic numerical measurement of vortex-stretching <br>alignment geometry across spatial dimensions n=2,3,5,10 <br>in the Navier-Stokes equations.</p> <p>The central finding is a viscosity-independent geometric <br>floor in θ_min — the minimum alignment angle between the <br>vorticity tensor and strain-vorticity interaction tensor — <br>that is specific to each dimension. In 3D this floor sits <br>at approximately 48°, is stable across ν=0.001 to 0.0001, <br>and is spatially pinned following a snap event at t*≈1.15.</p> <p>The paper states a precise conjecture: ∃ δ(n)>0 such that <br>θ_min(t) ≥ δ(n) for all smooth solutions. For n=3, proving <br>this conjecture would resolve the Millennium Problem.</p> |
| title | Dimensional Dependence of Vortex-Stretching Alignment in n-Dimensional Navier-Stokes Equations: Numerical Evidence for a Viscosity-Independent Geometric Floor and a Descent Strategy toward the Millennium Problem |
| topic | Analysis of PDEs Mathematics |
| url | https://doi.org/10.5281/zenodo.19640181 |