Multiscale Ceiling Structure of the He-Tu Antipodal Projection: A Fractal Decomposition Approach to Global H^s Boundedness for the 3D Navier-Stokes Equations
Abstract
Fifth paper in the He-Tu NS series. Introduces the Multiscale Ceiling Conjecture: each Littlewood-Paley layer Delta_j omega has an L^inf ceiling B_j = 2||Delta_j omega(0)||_{L^inf} non-increasing in time. If proved, immediately yields global H^s bound ||omega(t)||_{H^s} = 0, independent of t and mesh size h, resolving the 3D NS Millennium Problem. Proved results: global L^inf ceiling (Theorem 3.1), Bernstein localization (Lemma 3.2), conditional global H^s bound (Theorem 5.1). Numerical evidence: layer L^inf norms non-growing across 500 steps. Key obstacle: commutator estimate ||[Delta_j, P]omega||_{L^inf}
Fields of Study & Subjects
Navier-Stokes equation solutions
Advanced Mathematical Modeling in Engineering
Advanced Numerical Methods in Computational Mathematics
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 30 April 2026
- Document type
- Preprint