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Navier-Stokes Regularity as an Emergent Consequence of the 1/E^2 Entropic Suppression Law

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  • Stanley, Dustyn

Abstract

We present a unifying perspective in which the global regularity of the three-dimensional incompressible Navier–Stokes equations emerges naturally from a universal entropic suppression mechanism governed by a 1⁄E² decay law. Building on a recently completed proof of global existence and smoothness for initial data in Hˢ(ℝ³), with s > 5⁄2, we reinterpret the mathematical architecture through the lens of entropy-weighted coherence decay. We demonstrate that log-entropy dissipation, Gevrey-class smoothing, Lipschitz control, and Carleman-based uniqueness each instantiate components of an overarching physical law: high-energy localization is entropically suppressed according to an inverse-square energy scale. We propose this as a universal principle of entropic geometry underlying coherence protection across disciplines — including quantum field theory, general relativity, renormalization group flows, and turbulence.

Suggested Citation

  • Stanley, Dustyn, 2025. "Navier-Stokes Regularity as an Emergent Consequence of the 1/E^2 Entropic Suppression Law," OSF Preprints pq8bt_v1, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:pq8bt_v1
    DOI: 10.31219/osf.io/pq8bt_v1
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    1. Stanley, Dustyn, 2025. "Global Existence and Smoothness of Navier–Stokes Solutions," OSF Preprints xtvs2_v1, Center for Open Science.
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