[hal-00649051] Global Regularity of the 3D Axisymmetric Navier-Stokes Equations with swirl

In this paper we prove global regularity of the 3D axisymmetric Navier-Stokes equations with swirl To our knowledge our article answers to an open problem old of decades despite of great effort by many mathematicians and physicists Our proof is based on recent works about the surprising stabilizing effect of the convection term in the three-dimensional incompressible Navier-Stokes see HLEHLI and the interaction between the angular velocity and the angular vorticity fields see HLL Our proof uses also some estimates on the angular velocity uθ more precisely on ruθ that has been so far neglected



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