On the properties of affine solutions of cold plasma equations

2022/11/30 by Olga Rozanova, Rozanova, Olga, Marko Turzinsky +1
Mathematics · #35Q60 35L60 35L67 34M10 #Advanced Mathematical Physics Problems #Affine transformation #Analysis of PDEs (math.AP) #Axial symmetry #Classical mechanics #Differential Equations and Numerical Methods #Euler equations #Euler's formula #FOS: Mathematics #FOS: Physical sciences #Geometry #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Navier-Stokes equation solutions #Perturbation (astronomy) #Physics #Plasma #Poisson distribution #Quantum mechanics

paper · pdf · doi:10.48550/arxiv.2211.16894

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2022/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

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.

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