On Type I singularities of the local axi-symmetric solutions of the Navier-Stokes equations

TL;DR

This paper investigates the local regularity of axially symmetric Navier-Stokes solutions and demonstrates that, under specific natural conditions, Type I singularities do not occur.

Contribution

It proves the non-existence of Type I singularities in axially symmetric solutions under certain natural assumptions.

Findings

No Type I singularities under given conditions

Enhanced understanding of solution regularity

Potential implications for Navier-Stokes regularity conjecture

Abstract

Local regularity of axially symmetric solutions to the Navier-Stokes equations is studied. It is shown that under certain natural assumptions there are no singularities of Type I.