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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 500, Pages 67–73
DOI: https://doi.org/10.31857/S2686954321050131 (Mi danma205) 		 
MATHEMATICS

Existence and stability of equilibrium solutions of the Vlasov equation with a modified gravitational potential

T. V. Sal'nikova

Lomonosov Moscow State University, Moscow, Russia
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DOI: https://doi.org/10.31857/S2686954321050131
Abstract: We consider a system of mutually gravitating particles with possible collisions, which is modeled by supplementing the gravitational potential with the potential of repulsive forces similar to Lennard-Jones intermolecular forces. For an infinite number of particles, the probability density function is determined by the Vlasov kinetic equation with a modified gravitational potential. The existence of a large class of nonlinearly stable equilibrium solutions of this equation is proved using the energy–Casimir method.
Keywords: energy–Casimir method, nonlinear stability, Lennard-Jones type potential.
Presented: V. V. Kozlov
Received: 28.04.2021
Revised: 12.07.2021
Accepted: 18.08.2021
English version:
Doklady Mathematics, 2021, Volume 104, Issue 2, Pages 277–281
DOI: https://doi.org/10.1134/S1064562421050136
Bibliographic databases:
Document Type: Article
UDC: 531.19
Language: Russian
Citation: T. V. Sal'nikova, “Existence and stability of equilibrium solutions of the Vlasov equation with a modified gravitational potential”, Dokl. RAN. Math. Inf. Proc. Upr., 500 (2021), 67–73; Dokl. Math., 104:2 (2021), 277–281
Citation in format AMSBIB
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