Conditional Regularity for the Three-Dimensional Navier-Stokes Equations: Reduction to Critical Orlicz Entropy Propagation
Abstract
We prove that suitable weak solutions of the 3D Navier-Stokes equations with time-uniform critical Orlicz entropy control (L³log L velocity and L^(3/2)log L pressure) are smooth. This reduces the regularity problem to uniform propagation of a scaling-critical entropy functional. Physical approximation schemes eliminate spatial concentration defects, isolating temporal localization as the remaining obstruction. We formulate a precise hyperviscous entropy-control conjecture and identify two independent resolution paths.
Fields of Study & Subjects
Navier-Stokes equation solutions
Nonlinear Partial Differential Equations
Advanced Mathematical Physics Problems
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 4 January 2026
- Document type
- Preprint