  We study the affine solutions of the equations of plane oscillations of cold
plasma, which, under the assumption of electrostaticity, correspond to the
Euler-Poisson equations in the repulsive case. It is proved that the zero
equilibrium state of the cold plasma equations, both with and without the
assumption of electrostaticity, is unstable in the class of all affine
solutions. It is also shown that an arbitrary perturbation of an axially
symmetric electrostatic solution leads to a finite time blow-up.
