Study of instability for spherically symmetrical dynamic equilibrium states of self-gravitating Vlasov-Poisson gas Full article
| Source | Proceedings of the International Conference "Modern Achievements in Symmetries of Differential Equations" (Symmetry 2022). A Hybrid Conference. December 13-16, 2022. Suranaree University of Technology, Nakhon Ratchasima, Thailand Compilation, Отделение Московского центра фундаментальной и прикладной математики в ИПМ им. М.В. Келдыша РАН. Москва, https://keldysh.ru/math-center/conferences/symmetry2022.pdf.2023. 88 c. |
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| Output data | Year: 2023, Article number : A8, Pages count : 10 | ||||
| Tags | Vlasov-Poisson equations, spherical symmetry, stationary solutions, small perturbations, direct Lyapunov method, Antonov criterion, hydrodynamic substitution, gas-dynamic equations, Lyapunov functional, di erential inequality, a priori estimate, instability, analytical example | ||||
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Abstract:
This work considers the linear stability problem for spherically symmetrical states of dynamic equilibrium of a boundless collisionless self-gravitating Vlasov-Poisson gas with respect to perturbations of the same symmetry by the direct Lyapunov method. Using two changes of independent variables, the transition from kinetic equations to two in nite systems of gas-dynamic equations of the "vortex shallow water" type in the Boussinesq approximation was carried out, and absolute linear instability for the studied stationary solutions in the gas-dynamic description was proved. With the help of the fi rst version for change of independent variables, the formal nature of well-known Antonov criterion for linear stability of dynamic equilibrium states of self-gravitating stellar systems was discovered, so that this criterion is valid only with regard to some incomplete unclosed subclass of small perturbations. The same fundamental differential inequalities for the Lyapunov functionals were deduced in each case of independent variables replacement. Also, along with them, the constructive sufficient conditions for linear practical instability of the considered states of dynamic equilibrium with respect to spherically symmetrical perturbations were obtained.
Eventually, for both changes of independent variables, the a priori exponential estimates from below were found, and initial data was described for the studied small perturbations increasing in time. To con rm the results obtained, for the second version of independent variables replacement, analytical examples of the considered dynamic equilibrium states and small spherically symmetrical perturbations superimposed on them, which grow in time according to the found estimates, were constructed.
Cite:
Gubarev Y.
, Sun S.
Study of instability for spherically symmetrical dynamic equilibrium states of self-gravitating Vlasov-Poisson gas
In compilation Proceedings of the International Conference "Modern Achievements in Symmetries of Differential Equations" (Symmetry 2022). A Hybrid Conference. December 13-16, 2022. Suranaree University of Technology, Nakhon Ratchasima, Thailand. – Отделение Московского центра фундаментальной и прикладной математики в ИПМ им. М.В. Келдыша РАН., 2023. – C.76-85. РИНЦ
Study of instability for spherically symmetrical dynamic equilibrium states of self-gravitating Vlasov-Poisson gas
In compilation Proceedings of the International Conference "Modern Achievements in Symmetries of Differential Equations" (Symmetry 2022). A Hybrid Conference. December 13-16, 2022. Suranaree University of Technology, Nakhon Ratchasima, Thailand. – Отделение Московского центра фундаментальной и прикладной математики в ИПМ им. М.В. Келдыша РАН., 2023. – C.76-85. РИНЦ
Dates:
| Published online: | Oct 22, 2023 |
Identifiers:
| Elibrary: | 65650669 |
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