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April 11, 20260 citationsOpen Access

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

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IZIslem Zeroual

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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Cite This Study

Islem Zeroual (2026) studied this question.

synapsesocial.com/papers/69d9e58f78050d08c1b75bbchttps://doi.org/10.5281/zenodo.19484026
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