Global well-posedness for a rescaled Boussinesq system in critical Fourier-Besov spaces

TL;DR

This paper establishes the global well-posedness of a three-dimensional rescaled Boussinesq system within critical Fourier-Besov spaces, revealing how system behavior depends on viscosity and diffusivity parameters.

Contribution

It provides a novel global well-posedness result for the rescaled Boussinesq system in critical Fourier-Besov spaces, considering parameter-dependent initial conditions.

Findings

Global well-posedness proven for the rescaled Boussinesq system.

Behavior of solutions depends on viscosity and diffusivity relations.

Allows large initial norms under certain parameter conditions.

Abstract

In this work we prove a global well-posedness result for a tridimensional rescaled Boussinesq system, with positive full viscosity and diffusivity parameters in the framework of critical Fourier-Besov spaces. This rescaled approach permits to know the behaviour of the system according to relations between both the parameters and the initial velocity and temperature; for instance, it is possible to consider, for small enough viscosity and large diffusivity, a large enough critical Fourier-Besov norm for the initial temperature and it is also possible to consider, for small enough diffusivity and large viscosity, a large enough critical Fourier-Besov norm for both the velocity and the temperature.