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arXiv · 2201.11099

On the behavior of multidimensional axisymmetric solutions of the repulsive Euler-Poisson equations

Olga S. Rozanova
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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 $\bd=4$ 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 $t\to\infty$.

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Olga S. Rozanova. 2022-01-26. On the behavior of multidimensional axisymmetric solutions of the repulsive Euler-Poisson equations. https://doi.org/10.1016/j.physd.2022.133578

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