ИСТИНА

We study a version of the repulsive Euler-Poisson equations. Recently it was proved that the radially symmetric solutions of the repulsive Euler-Poisson equations with a non-zero background, blow up in many spatial dimensions except for $n=4$ 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 $t\to\infty$. We propose a technique for estimating the lifetime of a smooth solution in the case of electrostatic plasma oscillations in any dimensions, where radially symmetric solutions form a subclass. We compare the theoretical estimate with the existing results of numerical calculations.