Global Finite-Time Blowup Solutions to the 3D Navier–Stokes Equations via Initial Vorticity Contrast

This paper investigates the global finite-time blowup problem of smooth solutions for the three-dimensional incompressible Navier–Stokes equations. We construct a class of divergence-free, compactly supported smooth initial velocity fields with intrinsic spatial vorticity contrast. By establishing uniform persistence of vorticity spatial discrepancy via rigorous contradiction arguments and localized integral estimates of vortex stretch ing, boundary transport and viscous dissipation, we derive a modified Riccati-type differential inequality with explicit viscous damping terms for the vorticity magnitude functional. Under the standard BKM (Beale–Kato–Majda) blowup criterion, we prove that the constructed initial fields generate solutions that develop global finite-time sin gularity in the vorticity field. This work only confirms the existence of finite-time blowup paths and does not deny the global regularity of solutions for other admissible initial data. All derivations follow rigorous analytical frameworks without redundant empirical assumptions。

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-14
DOI
https://doi.org/10.5281/zenodo.23356268
Primary Topic
Navier-Stokes equation solutions
Type
preprint
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preprint

Global Finite-Time Blowup Solutions to the 3D Navier–Stokes Equations via Initial Vorticity Contrast

李詩明
Zenodo (CERN European Organization for Nuclear Research)
Navier-Stokes equation solutions
preprint

Global Finite-Time Blowup Solutions to the 3D Navier–Stokes Equations via Initial Vorticity Contrast

李詩明
preprint en

Abstract

This paper investigates the global finite-time blowup problem of smooth solutions for the three-dimensional incompressible Navier–Stokes equations. We construct a class of divergence-free, compactly supported smooth initial velocity fields with intrinsic spatial vorticity contrast. By establishing uniform persistence of vorticity spatial discrepancy via rigorous contradiction arguments and localized integral estimates of vortex stretch ing, boundary transport and viscous dissipation, we derive a modified Riccati-type differential inequality with explicit viscous damping terms for the vorticity magnitude functional. Under the standard BKM (Beale–Kato–Majda) blowup criterion, we prove that the constructed initial fields generate solutions that develop global finite-time sin gularity in the vorticity field. This work only confirms the existence of finite-time blowup paths and does not deny the global regularity of solutions for other admissible initial data. All derivations follow rigorous analytical frameworks without redundant empirical assumptions。

Zenodo (CERN European Organization for Nuclear Research)
Navier-Stokes equation solutions
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