We consider the classical Cauchy problem for a system of equations describing
3D arbitrary electrostatic oscillations of the cold plasma and introduce an
iteration procedure that allows estimating the blow-up time from below. This
procedure is constructive provided one succeed to obtain a two-sided estimate
of an additional quantity depending on the solution. We show that this is
possible in the case of one and two dimensions, as well as for solutions with
zero vorticity. For the particular case of two-dimensional initial data with
the radial symmetry, refined sufficient conditions for destruction and
preservation of smoothness in the first period of oscillations are obtained.
Moreover, we give the example of estimating the blow-up time for the data for
which results of numerics exist and discuss a roughness of our estimate.
