On Some Regularity Criteria for Axisymmetric Navier–Stokes Equations

We point out some criteria that imply regularity of axisymmetric solutions to Navier–Stokes equations. We show that boundedness of ‖ v r / r 3 ‖ L 2 ( R 3 × ( 0 , T ) ) as well as boundedness of ‖ ω φ / r ‖ L 2 ( R 3 × ( 0 , T ) ) , where v r is the radial component of velocity and ω φ is the angular component of vorticity, imply regularity of weak solutions.