Global Regularity for 3D Navier-Stokes via Restricted, NSE-Native Carleson Control at the Active Scale

Ira Feinstein

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Global Regularity for 3D Navier-Stokes via Restricted, NSE-Native Carleson Control at the Active Scale

Abstract

Ira Feinstein

We prove smooth continuation for the 3D incompressible Navier–Stokes equations with smooth initial data. The key innovation is a restricted, NSE-native Carleson estimate applied only at the active dyadic scale and only where the spectral gap and localized enstrophy allow. This stabilizes variable-axis conic multipliers (VACM), absorbs commutators into diffusion, and yields a non-circular endpoint Lyapunov inequality. Combining these tools we deduce the finiteness of the Beale–Kato–Majda
integral and obtain unconditional smooth continuation

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