Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
On the instability for one partial class of three-dimensional dynamic equilibrium states of the hydrogen Vlasov-Poisson plasma. / Gubarev, Yuriy; Ло, Цзинъюэ .
Analytical Methods in Differential Equations. De Gruyter Proceedings in Mathematics. Berlin : Walter de Gruyter GmbH, 2025. p. 121-130 13.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
}
TY - GEN
T1 - On the instability for one partial class of three-dimensional dynamic equilibrium states of the hydrogen Vlasov-Poisson plasma
AU - Gubarev, Yuriy
AU - Ло, Цзинъюэ
PY - 2025
Y1 - 2025
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/105021969728
UR - https://www.elibrary.ru/item.asp?id=80667110
U2 - 10.1515/9783111570518-013
DO - 10.1515/9783111570518-013
M3 - Conference contribution
SN - 9783111570518
SP - 121
EP - 130
BT - Analytical Methods in Differential Equations. De Gruyter Proceedings in Mathematics
PB - Walter de Gruyter GmbH
CY - Berlin
T2 - Всероссийская конференция «Математические проблемы механики сплошных сред», посвящённая 105-летию со дня рождения академика Л. В. Овсянникова
Y2 - 13 May 2024 through 17 May 2025
ER -
ID: 72698742