Global regularity for a family of 3D models of the axisymmetric Navier-Stokes equations

TL;DR

This paper proves the global regularity of a family of 3D axisymmetric Navier-Stokes models, showing that slightly stronger convection can stabilize solutions and prevent singularities.

Contribution

It introduces a family of modified models and demonstrates their global regularity, highlighting the stabilizing effect of increased convection strength.

Findings

Models are globally regular when convection is slightly stronger.

Stronger convection has a potential stabilizing effect.

Supports the idea that convection can prevent singularities in fluid models.

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.