Global regularity for a family of models of the axisymmetric Navier–Stokes system

In this paper, we investigate a family of 3D models for the axisymmetric incompressible Navier–Stokes system. The models are derived by changing the strength of convection and adding an stirring force. We show the global regularity when the strength of convection is stronger than that of the original Navier–Stokes system, which reveals the potential stabilization effect of convection. Our result answers an open problem in Hou–Liu–Wang (Nonlinearity 31:1940-1954, 2018).