Global regular axially-symmetric solutions to the Navier-Stokes equations. Part 1 (2304.00856v1)

Abstract: We prove existence of global regular axially-symmetric solutions to the Navier-Stokes equations in a cylindrical domain. We assume the periodic boundary conditions on the top and the bottom of the cylinder, but on the lateral part we assume vanishing of normal component of velocity, angular components of vorticity and angular component of velocity.