Geodesic
Existence and stability of equilibrium solutions of the Vlasov equation with a modified gravitational potential
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 67-73

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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. 
@article{DANMA_2021_500_a12,
     author = {T. V. Sal'nikova},
     title = {Existence and stability of equilibrium solutions of the {Vlasov} equation with a modified gravitational potential},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {67--73},
     publisher = {mathdoc},
     volume = {500},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_500_a12/}
}
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T. V. Sal'nikova. Existence and stability of equilibrium solutions of the Vlasov equation with a modified gravitational potential. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 67-73. http://geodesic.mathdoc.fr/item/DANMA_2021_500_a12/