Global well-posedness for Euler-Boussinesq system with critical dissipation

TL;DR

This paper establishes the global well-posedness of a fractional diffusion Boussinesq system coupling Euler equations with fractional diffusion for temperature, advancing understanding of such models with critical dissipation.

Contribution

It proves the global existence and uniqueness of solutions for a fractional diffusion Boussinesq system with critical dissipation, a novel result in this context.

Findings

Global well-posedness of the system is established.

The model incorporates fractional diffusion with critical dissipation.

Results contribute to the mathematical understanding of fluid dynamics with fractional operators.

Abstract

In this paper we study a fractional diffusion Boussinesq model which couples the incompressible Euler equation for the velocity and a transport equation with fractional diffusion for the temperature. We prove global well-posedness results.