Аннотация:It is proved that the radially symmetric solutions of the repulsive
Euler-Poisson equations with a non-zero background, corresponding to
cold plasma oscillations blow up in many spatial dimensions except for $\bd=4$ for
almost all initial data. The initial data, for which the solution may not blow up,
correspond to simple waves. Moreover, if a solution is globally smooth
in time, then it is either affine or tends to affine as
$t\to\infty$.