Interface Shell Law for Palinstrophy Non-Concentration and Defect Absorption in 3D Navier–Stokes Regularity (Volume II)

This record contains Volume II of a two-part study on conditional regularity for the 3D incompressible Navier–Stokes equations. Scope (what changes from Volume I):Volume I isolates three independent hypotheses needed to close a localized Constantin–Fefferman-type mechanism near a high-vorticity interface: (H1) direction coherence, (H2) geometric sparseness (subcritical packing / Minkowski dimension bound), and (H3) boundary-layer palinstrophy non-concentration used to absorb an interface defect term. Main contribution (Volume II):Instead of postulating (H3) directly, Volume II introduces an interface “shell law” for palinstrophy measured in dyadic distance shells around the high-vorticity interface. We prove that this shell law implies the strip non-concentration hypothesis (H3) as a lemma, with explicit constants and an exponent θ>0 (candidate θ = α* ≈ 1.27). Under sufficiently small strip ratio ρ/R, the interface defect becomes absorbable into viscous dissipation, and the conditional criterion of Volume I closes under the remaining hypotheses (H1)–(H2). Empirical / DNS validation protocol:We provide a reproducible protocol to measure both strip and shell observables on DNS data (Taylor–Green). On a Taylor–Green snapshot (N=256, R=1), free-slope fits yield θ̂_Φ ≈ 1.27–1.56 and θ̂_Ψ ≈ 2.58–3.11 across q ∈ {0.95, 0.97, 0.99} (OLS on k ∈ [1,5], with standard errors reported). Fixing θ=1.27 yields sup-constants C_{φ,sup} ≲ 0.65 and C_{ψ,sup} ≲ 0.61. Code and reproducibility:A companion GitHub repository contains scripts, generated tables and figures, and a minimal run pipeline:https://github.com/bsabljic/ns-ur-shell-law