TEBAC Navier--Stokes Program II: Vorticity-to-Shell Decomposition and Resonance Classification

This preprint is the second module of a modular TEBAC-based program toward the three-dimensional incompressible Navier--Stokes existence and smoothness problem. It continues the foundational Stokes--Galerkin--spectral-cascade framework developed in the preceding NS-I module and focuses on the next structural layer: the conversion of the large-data cascade residue into a precise vorticity-to-shell and resonance-classification ledger. The manuscript works on the periodic domain \(\mathbb T^3\). It records the vorticity equation, the enstrophy identity, the vortex-stretching production term, dyadic vorticity-shell balances, transport commutator residues, low--high / high--low / high--high interaction classes,…