A Conditional Proof of Spectral Flux Decay in 3D Navier–Stokes via Helical Decomposition and Geometric Frustration

This paper establishes a conditional decay estimate for the spectral flux in the three‑dimensional Navier–Stokes equations under a helicity‑dominance hypothesis. As stated in the abstract, “we prove a conditional estimate for the spectral flux Π (K) ” and “combined with the quasi‑trapping conditional regularity theorem of our previous work, this implies global regularity for the Navier–Stokes equations under the same helicity dominance hypothesis. ” The estimate shows that ∣Π (K) ∣≤C *E *E_ (>K) ¹/2 / K, where E>K is the energy above wavenumber K. Numerical evidence from earlier papers strongly supports the helicity‑dominance assumption.