A Slightly Supercritical Condition of Regularity of Axisymmetric Solutions to the Navier-Stokes Equations

TL;DR

This paper introduces a new regularity condition for axisymmetric solutions to the 3D Navier-Stokes equations that is slightly supercritical, advancing understanding of solution regularity in fluid dynamics.

Contribution

It establishes a novel regularity criterion for axisymmetric Navier-Stokes solutions that extends beyond critical thresholds, contributing to the mathematical theory of fluid flow.

Findings

Proves a new regularity condition for axisymmetric solutions.

Demonstrates the condition is slightly supercritical.

Provides insights into solution behavior under this criterion.

Abstract

In the note, a new regularity condition for axisymmetric solutions to the non-stationary 3D Navier-Stokes equations is proven. It is slightly supercritical.