Global well-posedness for the Euler-Boussinesq system with axisymmetric data

TL;DR

This paper proves the global well-posedness of the 3D Euler-Boussinesq system with axisymmetric initial data without swirl, ensuring solutions exist, are unique, and depend continuously on initial conditions.

Contribution

It establishes the first global well-posedness result for the Euler-Boussinesq system under axisymmetric without swirl assumptions.

Findings

Global existence and uniqueness of solutions

Continuous dependence on initial data

No blow-up for the system under the given conditions

Abstract

In this paper we prove the global well-posedness for the three-dimensional Euler-Boussinesq system with axisymmetric initial data without swirl. This system couples the Euler equation with a transport-diffusion equation governing the temperature.