Announcement of a Proof: Nikul the Real Equation for 3D Global Regularity

The global regularity of the 3D incompressible Navier-Stokes equations for large initial data is a foundational open problem in fluid mechanics. This extended preprint announces a rigorous analytical framework, Nikul the Real Equation, establishing global C^{\infty} regularity. By embedding the velocity field u(x,t) in a continuous time-weighted Nikul-Gevrey space and utilizing the explicit Topological Helicity Operator constrained strictly by the Cauchy-Schwarz inequality, we prove that non-linear vortex stretching is mathematically quenched. The framework incorporates Littlewood-Paley splitting and aligns topological phase cancellations with structural symmetries.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-04-26
DOI
https://doi.org/10.5281/zenodo.19786996
Primary Topic
Navier-Stokes equation solutions
Type
article
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article

Announcement of a Proof: Nikul the Real Equation for 3D Global Regularity

Nikulbhai Rajeshbhai Solanki
Zenodo (CERN European Organization for Nuclear Research)
Navier-Stokes equation solutions
article

Announcement of a Proof: Nikul the Real Equation for 3D Global Regularity

Nikulbhai Rajeshbhai Solanki
article en

Abstract

The global regularity of the 3D incompressible Navier-Stokes equations for large initial data is a foundational open problem in fluid mechanics. This extended preprint announces a rigorous analytical framework, Nikul the Real Equation, establishing global C^{\infty} regularity. By embedding the velocity field u(x,t) in a continuous time-weighted Nikul-Gevrey space and utilizing the explicit Topological Helicity Operator constrained strictly by the Cauchy-Schwarz inequality, we prove that non-linear vortex stretching is mathematically quenched. The framework incorporates Littlewood-Paley splitting and aligns topological phase cancellations with structural symmetries.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 4%
Navier-Stokes equation solutions
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