What question did this study set out to answer?

To provide a complete proof of the global regularity of the 3D incompressible Navier-Stokes equations.

April 11, 2026Open Access

Global Regularity of 3D Incompressible Navier-Stokes Equations: A Complete Proof via Orlicz-Zygmund Spectral Stability and Natural Damping Frequency

Key Points

To provide a complete proof of the global regularity of the 3D incompressible Navier-Stokes equations.
Removal of Remark 4.3 for clarity
Application of Lions' concentration-compactness principle
Utilization of Orlicz-Zygmund embeddings
Analysis of spectral properties of the Stokes operator
The core of the proof is entirely valid and unchanged
Global regularity is successfully established for the equations
Alignment with the spectral properties enhances understanding of the framework

Abstract

Version 3:This version removes Remark 4.3 from the previous draft to align the presentation with the spectral properties of the Stokes operator on the unbounded domain R³. The core proof of global regularity, based on Lions' concentration-compactness principle and Orlicz-Zygmund embeddings, remains unchanged and fully valid.

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