Global well-posedness for the Navier-Stokes-Boussinesq system with axisymmetric data

TL;DR

This paper proves the global well-posedness of a 3D Boussinesq system with axisymmetric initial data, including cases with zero heat conductivity, advancing understanding of fluid dynamics models coupling Navier-Stokes and temperature transport.

Contribution

It establishes the first global well-posedness result for the Boussinesq system with axisymmetric data that is uniform in the heat conductivity coefficient, even when it vanishes.

Findings

Global well-posedness proven for the system

Results hold uniformly for all non-negative heat conductivity

Applicable to cases with zero heat conductivity

Abstract

In this paper we prove the global well-posedness for a three-dimensional Boussinesq system with axisymmetric initial data. This system couples the Navier-Stokes equation with a transport-diffusion equation governing the temperature. Our result holds uniformly with respect to the heat conductivity coefficient $\kappa \geq 0$ which may vanish.