Stability of a thin disk with nearly rigid-body rotation

The instability of a rotating gaseous disk immersed in a galaxy or, more generally, in a system with large mass, is considered. Specifically, the existence of an entropy gradient in the gas is assumed, and slow instabilities resulting from this nonuniformity of the medium are selected out for study. It is shown that this type of instability is absent in a perfect gas, but appears in the presence of hysteresis, if a certain inequality holds.