Study of the stability for three-dimensional states of dynamic equilibrium of the electron Vlasov-Poisson gas
Научная публикация
| Журнал |
AIP Conference Proceedings
ISSN: 0094-243X
|
| Вых. Данные |
Год: 2023,
Том: 2872,
Номер статьи
: 060024,
Страниц
: 7
DOI:
10.1063/5.0163155
|
| Авторы |
Gubarev Yuriy G.
1,2
,
Liu Yang
2
|
| Организации |
| 1 |
Laboratory for Fluid and Gas Vortex Motions, Lavrentyev Institute for Hydrodynamics, Novosibirsk, 630090, Russian Federation
|
| 2 |
Department for Differential Equations, Novosibirsk State University, Novosibirsk, 630090, Russian Federation
|
|
Информация о финансировании (2)
|
1
|
Министерство науки и высшего образования Российской Федерации
|
FWGG-2021-0008
|
|
2
|
Министерство науки и высшего образования Российской Федерации
|
FWGG-2021-0004
|
Here, in this paper, the spatial motions of a boundless collisionless electron Vlasov-Poisson gas were considered in a three-dimensional Cartesian coordinate system. Using the replacing of independent variables in the form of hydrodynamic substitution, a transition was made from the kinetic equations to an infinite system of gas-dynamic equations in the “vortex shallow water” and the Boussinesq approximations. In the process of proving the linear instability for the exact stationary solutions to the Vlasov-Poisson equations, the well-known sufficient Newcomb-Gardner-Rosenbluth condition for stability of these solutions with respect to one incomplete unclosed particular class of small spatial perturbations was reversed. An original linear differential second-order inequality with constant coefficients for the Lyapunov functional was also obtained. When the sufficient conditions found in this paper for the linear practical instability of the exact stationary solutions under research are satisfied, an a priori exponential estimate from below for the growth of small three-dimensional perturbations follows from this inequality. Since the estimate was derived without any additional restrictions on the exact stationary solutions under study, then, in this way, the absolute linear instability for the spatial dynamic equilibrium states of the electron Vlasov-Poisson gas with respect to three-dimensional
perturbations was proved.