Local Regularity of Axisymmetric Solutions to the Navier-Stokes Equations}

TL;DR

This paper establishes a local regularity condition for axisymmetric solutions to the 3D Navier-Stokes equations, showing they do not exhibit Type I blowups, thus contributing to understanding solution regularity.

Contribution

It proves that axially symmetric energy solutions to the Navier-Stokes equations cannot have Type I blowups, advancing regularity theory for these solutions.

Findings

Axisymmetric energy solutions have no Type I blowups.

A new local regularity condition is established.

Supports the conjecture of regularity in axisymmetric flows.

Abstract

In the note, a local regularity condition for axisymmetric solutions to the non-stationary 3D Navier-Stokes equations is proven. It reads that axially symmetric energy solutions to the Navier-Stokes equations have no Type I blowups.