Regularity criteria and uniform estimates for the Boussinesq system with   the temperature-dependent viscosity and thermal diffusivity
  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. 
Jishan Fan, Fucai Li and Gen Nakamura
math.AP math-ph math.MP