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.