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Preprint . 2025
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
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Global Regularity for the 3D Incompressible Navier–Stokes Equations via Emergent Nonlinear Vorticity Dissipation

Authors: Polozov, Andrei;

Global Regularity for the 3D Incompressible Navier–Stokes Equations via Emergent Nonlinear Vorticity Dissipation

Abstract

We establish the global existence, smoothness, and uniqueness of solutions to the three- dimensional incompressible Navier–Stokes equations, for smooth divergence-free initial data and in the absence of external forcing. The result holds uniformly on both the whole space and the periodic domain. The analysis makes no assumptions on smallness, symmetry, or decay at infinity. The key mechanism is a nonlinear damping effect that arises intrinsically from the classical viscous term through a directional decomposition of the vorticity field. This emergent dissipation suppresses vortex stretching and prevents the concentration of energy at small scales. The proof combines spectral energy estimates, Sobolev and Gevrey-class regularity theory, compactness arguments, and strong convergence of approximate solutions. All known blow-up mechanisms—including those based on self-similarity, intermittent turbulence, and convex integration—are rigorously excluded. This work provides a complete and self-contained resolution of the global regularity prob- lem for three-dimensional incompressible Navier–Stokes flows, entirely within the unmodified classical formulation.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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