On the behavior of multidimensional radially symmetric solutions of the repulsive Euler-Poisson equations

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 -> infinity.(c) 2022 Elsevier B.V. All rights reserved.