the Three-Dimensional Navier–Stokes Equations via Helical Decomposition and Kinematic Barrier
Author: Ash Danner — Emanation Interactive LLC
Status: Submitted to Annals of Mathematics, March 10, 2026
We prove that smooth, finite-energy axisymmetric solutions of the three-dimensional incompressible Navier–Stokes equations remain smooth for all time. The proof introduces a helicity-based decomposition, reduces the critical case to swirl via a topological surgery argument, then eliminates blow-up through a 5D lifting and barrier method. The ancient limit is ruled out by the Koch–Nadirashvili–Seregin–Šverák Liouville theorem.
AI tools were used collaboratively in the development of this work. The corresponding author has independently verified every theorem, proof, and proposition, and takes full responsibility for all contents of the manuscript. Full details appear in the Acknowledgments section.
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