Global regular axially symmetric solutions to the Navier-Stokes equations in a periodic cylinder

TL;DR

This paper proves the existence of global regular axially symmetric solutions with large swirl for the Navier-Stokes equations in a periodic cylinder, under slip boundary conditions, by extending local solutions and controlling initial data.

Contribution

It establishes the global regularity of solutions with large swirl in a cylindrical domain, extending previous local results under slip boundary conditions.

Findings

Global regular solutions are proven to exist for large swirl.

The solutions are valid in a periodic cylinder with slip boundary conditions.

The proof involves extending local solutions and ensuring initial data do not increase.

Abstract

Global regular axially symmetric solutions with large swirl in a cylinder with periodic conditions on the top and on the bottom are proved. On the lateral part of its boundary the boundary slip conditions are assumed. The proof is obtained step by step extending a local solution and showing that the initial data are not increasing.