Abstract: In this paper, we use a mathematical model for the two-component Vlasov–Poisson plasma to investigate the stability for one subclass of spatial states of plasmic dynamic equilibrium against small three-dimensional (3D) perturbations. The Newcomb–Gardner–Rosenbluth sufficient condition for linear stability of exact stationary solutions to the Vlasov–Poisson equations is reversed, and its formal character is revealed. Then, for spatial states of dynamic equilibrium of hydrogen Vlasov–Poisson plasma, sufficient conditions for linear practical instability are obtained regarding 3D perturbations. Applying the direct Lyapunov method, we demonstrate that spatial dynamic equilibria of two-component Vlasov–Poisson plasma are absolutely unstable with respect to small 3D perturbations. The a priori exponential estimate from below is constructed for one partial class of small spatial perturbations of exact stationary solutions to new defining equations of the gas-dynamic type, which grow over time and are described by the field of Lagrangian displacement. Analytical examples for exact stationary solutions to the Vlasov–Poisson equations and growing small 3D perturbations superimposed on these solutions are presented.

Cite: Gubarev Y. , Luo J.
On the instability for one partial class of three-dimensional dynamic equilibrium states of the hydrogen Vlasov-Poisson plasma
In compilation Analytical Methods in Differential Equations. – De Gruyter., 2025. – C.121-130. – ISBN 9783111570518. DOI: 10.1515/9783111570518-013

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Published print:	Feb 17, 2025
Published online:	Feb 17, 2025

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