Exact shell commutators, loss-controlled compression, and vorticity occupation bounds for the hyperdissipative Navier–Stokes equations
Year: 2026
Type: preprint
Abstract: A self-contained shell-resolved proof of global smooth well-posedness for the three-dimensional periodic Navier–Stokes equations with fractional dissipation ν(−Δ)^α in the strict hyperdissipative range α > 5/4. The regularity range is classical (Lions, 1969); the contribution is a different proof architecture. The central object is a full-advector source–recipient transfer ledger that is exactly pairwise antisymmetric, so every weighted shell-energy balance becomes an exact commutator involving only differences of shell weights. A single nonlinear estimate with explicit constants, fixed-scale absorption above a viscosity-dependent shell, and a vorticity occupation-tail bound yield the Galerkin-uniform Beale–Kato–Majda integral. A direct W^{1,∞} continuation estimate, integer Sobolev transport bound, compactness argument, and uniqueness proof give a fully internal Galerkin limit. Also recorded: exact compression–defect and switching-cost identities, a Gram-matrix channel-rank guard, and a localized three-wall defect criterion valid for all α ≥ 1. Finite-dimensional computations (including cross-backend A100 CPU/GPU verification) are included as an independent calibration and are not used in the proof. Package contents: LaTeX source, compiled PDF (30 pages, 5 figures, 7 tables), cover letter, 600 dpi production artwork, Online Resource 1 (reproducibility package with production code, diagnostic arrays, threshold tables, SHA-256 manifests), and a complete audit trail (mathematical preservation, build/preflight, JMFM compliance, figure audit, data synchronization ledger). No conclusion for the classical case α = 1 is claimed.
Author: Novgorodtsev, Aleksei
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203952088
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