On the properties of multidimensional electrostatic oscillations of an electron plasma

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