On the stability of a particular class of one-dimensional states of dynamic equilibrium of the Vlasov–Poisson electron gas
The one-dimensional problem of the linear stability of dynamic states of local thermodynamic equilibria with respect to small perturbations was studied for the case when the Vlasov–Poisson electron gas contains electrons with a stationary distribution function that is constant in physical space and...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2024-04-01
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| Series: | Учёные записки Казанского университета. Серия Физико-математические науки |
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| Online Access: | https://uzakufismat.elpub.ru/jour/article/view/37 |
| _version_ | 1797205439913394176 |
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| author | Yu. G. Gubarev M. S. Kotelnikova |
| author_facet | Yu. G. Gubarev M. S. Kotelnikova |
| author_sort | Yu. G. Gubarev |
| collection | DOAJ |
| description | The one-dimensional problem of the linear stability of dynamic states of local thermodynamic equilibria with respect to small perturbations was studied for the case when the Vlasov–Poisson electron gas contains electrons with a stationary distribution function that is constant in physical space and variable in a continuum of velocities. The absolute instability of all considered one-dimensional dynamic states of any local thermodynamic equilibrium was proved using the direct Lyapunov method. The scope of applicability of the Newcomb–Gardner–Rosenbluth sufficient condition for linear stability was outlined. An a priori exponential estimation was obtained for the rise of small one-dimensional perturbations from below. Analytic counterexamples to the spectral Newсomb–Gardner theorem and the Penrose criterion were constructed. Earnshaw’s theorem was extended from classical mechanics tostatistical one. |
| first_indexed | 2024-04-24T08:51:09Z |
| format | Article |
| id | doaj.art-9076ba62da72473ca1e8e07a410173a3 |
| institution | Directory Open Access Journal |
| issn | 2541-7746 2500-2198 |
| language | English |
| last_indexed | 2024-04-24T08:51:09Z |
| publishDate | 2024-04-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета. Серия Физико-математические науки |
| spelling | doaj.art-9076ba62da72473ca1e8e07a410173a32024-04-16T11:42:17ZengKazan Federal UniversityУчёные записки Казанского университета. Серия Физико-математические науки2541-77462500-21982024-04-011661365110.26907/2541-7746.2024.1.36-5132On the stability of a particular class of one-dimensional states of dynamic equilibrium of the Vlasov–Poisson electron gasYu. G. Gubarev0M. S. Kotelnikova1Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of SciencesLavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of SciencesThe one-dimensional problem of the linear stability of dynamic states of local thermodynamic equilibria with respect to small perturbations was studied for the case when the Vlasov–Poisson electron gas contains electrons with a stationary distribution function that is constant in physical space and variable in a continuum of velocities. The absolute instability of all considered one-dimensional dynamic states of any local thermodynamic equilibrium was proved using the direct Lyapunov method. The scope of applicability of the Newcomb–Gardner–Rosenbluth sufficient condition for linear stability was outlined. An a priori exponential estimation was obtained for the rise of small one-dimensional perturbations from below. Analytic counterexamples to the spectral Newсomb–Gardner theorem and the Penrose criterion were constructed. Earnshaw’s theorem was extended from classical mechanics tostatistical one.https://uzakufismat.elpub.ru/jour/article/view/37vlasov–poisson electron gasdynamic equilibrium stateslinear stabilitydirect lyapunov method |
| spellingShingle | Yu. G. Gubarev M. S. Kotelnikova On the stability of a particular class of one-dimensional states of dynamic equilibrium of the Vlasov–Poisson electron gas Учёные записки Казанского университета. Серия Физико-математические науки vlasov–poisson electron gas dynamic equilibrium states linear stability direct lyapunov method |
| title | On the stability of a particular class of one-dimensional states of dynamic equilibrium of the Vlasov–Poisson electron gas |
| title_full | On the stability of a particular class of one-dimensional states of dynamic equilibrium of the Vlasov–Poisson electron gas |
| title_fullStr | On the stability of a particular class of one-dimensional states of dynamic equilibrium of the Vlasov–Poisson electron gas |
| title_full_unstemmed | On the stability of a particular class of one-dimensional states of dynamic equilibrium of the Vlasov–Poisson electron gas |
| title_short | On the stability of a particular class of one-dimensional states of dynamic equilibrium of the Vlasov–Poisson electron gas |
| title_sort | on the stability of a particular class of one dimensional states of dynamic equilibrium of the vlasov poisson electron gas |
| topic | vlasov–poisson electron gas dynamic equilibrium states linear stability direct lyapunov method |
| url | https://uzakufismat.elpub.ru/jour/article/view/37 |
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