A priori estimate for axially symmetric solutions to the Navier-Stokes equations near the axis of symmetry

TL;DR

This paper derives a priori estimates for axially symmetric Navier-Stokes solutions with large swirl in a periodic cylinder, which are crucial for proving the existence of global regular solutions.

Contribution

It provides new a priori estimates for solutions with large swirl, advancing understanding of global regularity in axially symmetric Navier-Stokes flows.

Findings

A priori estimates established for solutions with large swirl

Results applicable to solutions in a periodic cylinder with boundary slip

Supports proof of global regularity for axially symmetric solutions

Abstract

The axially symmetric solutions to the Navier-Stokes equations in a periodic cylinder with boundary slip conditions on the lateral part of its boundary are considered. A priori estimates for solutions with large swirl necessary for a proof of global regular solutions are derived.