On Some Regularity Criteria for Axisymmetric Navier–Stokes Equations

Abstract

We point out some criteria that imply regularity of axisymmetric solutions to Navier–Stokes equations. We show that boundedness of ‖vr/r3‖L2(R3×(0,T)) as well as boundedness of ‖ωφ/r‖L2(R3×(0,T)), where vr is the radial component of velocity and ωφ is the angular component of vorticity, imply regularity of weak solutions.