Global regularity for a family of 3D models of the axi-symmetric Navier–Stokes equations

Abstract

We consider a family of 3D models for the axi-symmetric incompressible Navier-Stokes equations. The models are derived by changing the strength of the convection terms in the axisymmetric Navier-Stokes equations written using a set of transformed variables. We prove the global regularity of the family of models in the case that the strength of convection is slightly stronger than that of the original Navier-Stokes equations, which demonstrates the potential stabilizing effect of convection.

Finite-time blowup for the inviscid vortex stretching equation

“…Hou et al proved finite-time blowup for these axisymmetric equations with vorticity neglected [14]. See also [12,15,16] for further work on this scenario. In particular, Hou, Liu, and Wang proved global regularity for the viscous case of the these equations when the advection term is strengthened [16].…”

“…See also [12,15,16] for further work on this scenario. In particular, Hou, Liu, and Wang proved global regularity for the viscous case of the these equations when the advection term is strengthened [16].…”