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Existence and Stability of Equilibrium Solutions of the Vlasov Equation with a Modified Gravitational Potential

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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.

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ACKNOWLEDGMENTS

The author is grateful to Gerhard Rein for helpful discussion of this work.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119991, Moscow, Russia

    T. V. Salnikova

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  1. T. V. Salnikova
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Correspondence to T. V. Salnikova.

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Translated by I. Ruzanova

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Salnikova, T.V. Existence and Stability of Equilibrium Solutions of the Vlasov Equation with a Modified Gravitational Potential. Dokl. Math. 104, 277–281 (2021). https://doi.org/10.1134/S1064562421050136

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  • DOI: https://doi.org/10.1134/S1064562421050136

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