Stability of a contracting flat model stellar system of finite radius

An exact, self-consistent, nonlinear model of a contracting, pressure-free stellar system having the form of a nonrotating, finite-radius disk is constructed in the Newtonian approximation. This nonstationary model is tested for stability against asymmetric perturbations. For all perturbation modes other than the trivial harmonics, power-law Jeans instability will develop, disrupting the self-similar collapse process and causing the disk to break into separate pieces