Year: 2026
Type: preprint
Abstract: For smooth finite-energy axisymmetric Navier--Stokes solutions with swirl, we give a continuation criterion in terms of the signed cumulative work of the actual post-cut source-generated meridional current, with quartic viscous dissipation counted once. In the stated strong Sobolev class the criterion is necessary and sufficient and requires neither a global circulation bound nor spatial moments. We also prove cumulative inward-compression criteria, collect quantitative necessary conditions at a first singular time, and give a complete-history mixed-residual test for noncontinuation. Auxiliary results quantify quartic dissipation, energy-funded source bounds, and causal source--receiver identities. An explicit smooth whole-space datum has positive newborn source production.
Source: arXiv (Cornell University)
Author: Shahmurov, Rishad
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223018744