What question did this study set out to answer?

The study aims to establish global regularity for a truncated version of the Navier–Stokes equations and to explain the significance of access to high frequencies.

January 18, 2026Open Access

Global Regularity of Band-Limited Navier–Stokes Equations

Key Points

The study aims to establish global regularity for a truncated version of the Navier–Stokes equations and to explain the significance of access to high frequencies.
Proved global regularity for a spectrally truncated version of the Navier-Stokes equations
Utilized standard energy estimates
Applied Bernstein inequality
Demonstrated that global regularity can be achieved for band-limited Navier-Stokes equations
Clarified the role of high-frequency access in singularity formation in the full equations

Abstract

This short technical note proves global regularity for a spectrally truncated (band-limited) version of the three-dimensional incompressible Navier–Stokes equations. The result is elementary and relies on standard energy estimates and the Bernstein inequality. The purpose of the note is pedagogical: to clarify why access to arbitrarily high frequencies is essential for potential singularity formation in the full Navier–Stokes equations.

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Cite This Study

Łukasz Bojanowski (Fri,) studied this question.

synapsesocial.com/papers/696c785beb60fb80d13967e3 https://doi.org/https://doi.org/10.5281/zenodo.18269782

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