  We consider equations of the type: \[\partial_t \omega = \omega R(\omega),\]
for general linear operators $R$ in any spatial dimension. We prove that such
equations almost always exhibit finite-time singularities for smooth and
localized solutions. Singularities can even form in settings where solutions
dissipate an energy. Such equations arise naturally as models in various
physical settings such as inviscid and complex fluids.
