Abstract
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 d=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→∞.
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