Conditional Regularity for the Three-Dimensional Navier-Stokes Equations: Reduction to Critical Orlicz Entropy Propagation

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Authors: Giovanni Esposito
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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