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Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions

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Abstract

Rigorous results on the stability of stationary solutions of the Vlasov-Poisson system are obtained in the contexts of both plasma physics and stellar dynamics. It is proved that stationary solutions in the plasma physics (stellar dynamics) case are linearly stable if they are decreasing (increasing) functions of the local, i.e., particle, energy. The main tool in the analysis is the free energy, a conserved quantity of the linearized system. In addition, an appropriate global existence result is proved for the linearized Vlasov-Poisson system and the existence of stationary solutions which satisfy the above stability condition is established.

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Authors and Affiliations

  1. Mathematisches Institut der Universität München, Theresienstr. 39, 80333, München

    Jürgen Batt, Philip J. Morrison & Gerhard Rein

  2. Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, 78712, Austin, Texas

    Jürgen Batt, Philip J. Morrison & Gerhard Rein

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  1. Jürgen Batt
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  2. Philip J. Morrison
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  3. Gerhard Rein
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Communicated by P. Holmes

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Batt, J., Morrison, P.J. & Rein, G. Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions. Arch. Rational Mech. Anal. 130, 163–182 (1995). https://doi.org/10.1007/BF00375154

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