A Sufficient Condition for Instability in the Limit of Vanishing Dissipation

A general theorem is presented concerning an evolution PDE whose leading-order term is of viscous dissipative type. It is proved that, under certain conditions, instability in the underlying nondissipative equation is a sufficient condition for viscous instability in the limit of vanishing viscosity. This theorem is applied to give a sufficient condition for instability of a rotating body with a cavity filled by a viscous fluid.