Temperature variations leave the formation and stability of velocity singularities unchanged in the hydrostatic Boussinesq system for both inviscid and vertically diffusive temperature cases.
Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics.Annals of Mathematics, 166(1):245–267, July 2007
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On the Profile of Singularity Formation for the Incompressible Hydrostatic Boussinesq system
Temperature variations leave the formation and stability of velocity singularities unchanged in the hydrostatic Boussinesq system for both inviscid and vertically diffusive temperature cases.