Temperature variations leave the formation and stability of velocity singularities unchanged in the hydrostatic Boussinesq system for both inviscid and vertically diffusive temperature cases.
Blowup of solutions of the hydrostatic euler equations.Proceedings of the American Mathe- matical Society, 143(3):1119–1125, November 2014
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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.