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The aim is to prove global regularity of 3D incompressible Navier-Stokes equations with smooth initial conditions.

February 2, 2026Open Access

Global Regularity of 3D Navier-Stokes via the Alignment Gap Mechanism

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The aim is to prove global regularity of 3D incompressible Navier-Stokes equations with smooth initial conditions.
Analyzed vorticity-strain coupling dynamics.
Used the Beale-Kato-Majda criterion to establish global regularity.
Validated findings through direct numerical simulations (DNS).
Derived results from the hydrodynamic limit of the Tamesis Kernel Hamiltonian.
Confirmed global regularity as per the established theorem.
Observed alignment gap coefficient ⟨α1⟩ ≈ 0.15, well below the critical threshold for singularity.
Established viscosity as a 'thermodynamic censor' preventing singularity formation.

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Mathematical proof demonstrates global regularity in 3D Navier-Stokes equations, indicating a significant breakthrough.

Douglas H. M. FULBER (2026) studied this question.

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