Year: 2026
Type: preprint
Abstract: We examine the proof of Dongyi Wei's logarithmic circulation criterion. A trace estimate specific to $\nabla(u_r/r)$ replaces a generic squared-swirl form bound by one with one logarithm rather than two. Repeating the coupled $J$--$Ω$ energy and comparison argument then gives a proposed threshold of order $(\log D)^{-5/4}$. Under the hypotheses stated below, the proof is intended to establish regularity when $|r u_θ|\le C|\log r|^{-α}$ uniformly near the axis with $α>5/4$, and at $α=5/4$ with an absolute sufficiently small coefficient. Every analytic step, including the cutoff core and exterior terms, is included for independent checking.
Source: arXiv (Cornell University)
Author: Zhou, Daoguo
Institution: Hangzhou Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223408302