Regularity criteria and uniform estimates for the Boussinesq system with the temperature-dependent viscosity and thermal diffusivity

TL;DR

This paper develops regularity criteria and uniform estimates for the 3D Boussinesq system with temperature-dependent properties, and provides uniform estimates for the 2D case with constant viscosity.

Contribution

It introduces new regularity criteria for the 3D Boussinesq system with variable properties and uniform estimates for the 2D case with constant viscosity.

Findings

Regularity criteria for 3D Boussinesq system with temperature-dependent viscosity.

Uniform estimates for 2D Boussinesq system with constant viscosity.

Enhanced understanding of the system's behavior under different conditions.

Abstract

In this paper we establish some regularity criteria for the 3D Boussinesq system with the temperature-dependent viscosity and thermal diffusivity. We also obtain some uniform estimates for the corresponding 2D case when the fluid viscosity coefficient is a positive constant.