Global well-posedness for a Boussinesq- Navier-Stokes System with critical dissipation

TL;DR

This paper proves the global existence and uniqueness of solutions for a fractional diffusion Boussinesq system, coupling Navier-Stokes equations with fractional dissipation and a temperature transport equation, even with rough initial data.

Contribution

It establishes the first global well-posedness results for a Boussinesq system with critical fractional dissipation and rough initial conditions.

Findings

Global well-posedness for the system with rough initial data

Existence and uniqueness of solutions in critical fractional dissipation setting

Extension of classical results to fractional diffusion models

Abstract

In this paper we study a fractional diffusion Boussinesq model which couples a Navier-Stokes type equation with fractional diffusion for the velocity and a transport equation for the temperature. We establish global well-posedness results with rough initial data.