What question did this study set out to answer?

The aim is to develop a finite-time blow-up framework for the 3D Navier-Stokes equations, examining conditions leading to solution divergence.

March 28, 2026Open Access

Navier–Stokes 3D Unmodified Сoncrete Finite-Time Blow-up Framework

Key Points

The aim is to develop a finite-time blow-up framework for the 3D Navier-Stokes equations, examining conditions leading to solution divergence.
Proposed a quantitative framework for analyzing Navier-Stokes equations.
Combined localized enstrophy barriers with geometric-spectral strain bounds.
Introduced a topological coercivity channel for analysis.
Defined internally closed block conditions for the constructed data class.
Demonstrated divergence of the BKM integral under proposed conditions.
Excluded smooth continuation of solutions beyond finite time for specific data classes.

Abstract

This preprint proposes a quantitative finite-time blow-up framework for the 3D incompressible Navier-Stokes equations in R³. The analysis combines localized enstrophy barriers, geometric-spectral strain lower bounds, and a topological coercivity channel. Under the internally closed block conditions stated in the manuscript, the framework yields divergence of the BKM integral and excludes smooth continuation beyond finite time for the constructed data class.

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