On the properties of affine solutions of cold plasma equations

TL;DR

This paper investigates the stability of affine solutions in cold plasma equations, demonstrating that the zero equilibrium state is unstable and that perturbations can cause finite time blow-up, highlighting critical behaviors in plasma dynamics.

Contribution

The study provides new insights into the instability and blow-up phenomena of affine solutions in cold plasma equations, extending understanding of plasma oscillation behaviors.

Findings

Zero equilibrium state is unstable in affine solutions.

Perturbations of electrostatic solutions lead to finite time blow-up.

Instability occurs both with and without electrostatic assumptions.

Abstract

We study the affine solutions of the equations of plane oscillations of cold plasma, which, under the assumption of electrostaticity, correspond to the Euler-Poisson equations in the repulsive case. It is proved that the zero equilibrium state of the cold plasma equations, both with and without the assumption of electrostaticity, is unstable in the class of all affine solutions. It is also shown that an arbitrary perturbation of an axially symmetric electrostatic solution leads to a finite time blow-up.