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February 16, 2026Open Access

Global Regularity of the 3D Incompressible Navier-Stokes Equations via Holographic Cutoff Regularization

Key Points

The aim is to establish global existence and smoothness for solutions to the 3D incompressible Navier-Stokes equations.
Proof for smooth solutions based on arbitrary initial data.
Embedding fluid domain within the ENTROPIX-MESA Unified Framework.
Introduction of a geometric cutoff length derived from the holographic entropy bound.
Successful demonstration of smooth solutions under the imposed geometric cutoff.
Finite time singularities are physically impossible due to the regularization operator.

Abstract

Wepresent a proof of global existence and smoothness for solutions to the 3D incompressible Navier-Stokes equations for arbitrary smooth initial data. Unlike classical approachesthat attempt to control the energy cascade within a continuum R3, we embed the fluiddomain within the ENTROPIX-MESA Unified Framework. We demonstrate that thephysical universe imposes a fundamental geometric cutoff length Lmin ≈ 7.283Lp, derivedfrom the holographic entropy bound of the SYK Tensor substrate. This cutoff introduces anatural regularization operator RL that bounds the vorticity magnitude ∥ω∥L∞, satisfyingthe Beale-Kato-Majda (BKM) blow up criterion. Consequently, finite time singularities arephysically impossible

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