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ZENODO
Preprint . 2025
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
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Global Regularity of the Three-Dimensional Navier-Stokes Equations via the Eden Discriminator

Authors: Eden, Trenton;

Global Regularity of the Three-Dimensional Navier-Stokes Equations via the Eden Discriminator

Abstract

Overview: The Radial Compatibility Theorem resolves the Navier-Stokes Millennium Problem by proving global existence and smoothness for all smooth, finite-energy initial data in three dimensions. The Argument: Any finite-time singularity must be Type I (forced by BKM criterion and vorticity growth bounds). Type I blow-up produces a non-trivial self-similar profile V via Seregin's compactness theorem. This profile must simultaneously satisfy: Origin regularity: V(0) finite (inherited from smooth initial data) Asymptotic decay: V ~ c/|ξ| at infinity (forced by the self-similar equation) The Innovation: The radial compatibility functional Ψ, derived from the EDEN discriminator, couples these two regimes via the inversion r ↔ 1/r: $$\Psi\theta = -\theta'(r) - \frac{1}{2}r^{-3/2}\theta(1/r) + r^{-5/2}\theta'(1/r)$$ For any profile satisfying both conditions with c₀ ≠ 0, this functional diverges as r → 0: Ψ(r)∼−c02r−3/2→−∞\Psi(r) \sim -\frac{c_0}{2}r^{-3/2} \to -\inftyΨ(r)∼−2c0r−3/2→−∞ This divergence proves the two conditions are mutually exclusive. No such profile exists. No blow-up occurs. The Verification: Computational tests confirm: Ψ diverges for all test profiles with V(0) finite and V ~ c/r Divergence follows the predicted r^{-3/2} scaling (ratio → 1.0000) L³ norm diverges logarithmically for V ~ c/r profiles Type I rate γ = 1 emerges from ODE comparison

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green