Global Vorticity Boundedness via He-Tu Antipodal Projection: H^s Uniform Bounds, Weak-Strong Convergence, and Nonlinear Closure for the 3D Navier-Stokes Equations
Abstract
v2 adds four new theorems completing the local-in-time lattice-to-continuum program. (i) P is H^s-non-expansive for all s>=0, via affine commutativity D^alpha P = P D^alpha. (ii) H^s uniform bound: ||omega_h(t)||_{H^s} L^inf (s>3/2) yields L^inf bound uniform in h. (iv) Banach-Alaoglu + Aubin-Lions gives weak then strong L^2([0,T];H^{s-1}) convergence; nonlinear closure (omega_h cdot nabla) u_h -> (omega cdot nabla) u is established. The single remaining gap is Conjecture 6.1: global H^s bound on [0,inf), which is equivalent to the Navier-Stokes Millennium Problem.
Fields of Study & Subjects
Navier-Stokes equation solutions
Advanced Mathematical Physics Problems
Computational Fluid Dynamics and Aerodynamics
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 30 April 2026
- Document type
- Preprint