  We apply the convection stability criterion to a fluid in global
thermodynamic equilibrium with a rigid rotation or with a constant acceleration
along the streamlines. Different equations of state describing strongly
interacting matter are considered and for each of them the analysed system is
found to be stable with respect to convection. This finding brings new evidence
for physical relevance of non-static global equilibrium states. Our results can
be directly used for other similar media to check their convective stability.
