Global Vorticity Boundedness via He-Tu Antipodal Projection: H^s Uniform Bounds, Weak-Strong Convergence, and Nonlinear Closure for the 3D Navier-Stokes Equations

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Authors: Yao-Kai Kao
Cited by: 2
References: 3

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