Rigorous results on the stability of stationary solutions of the Vlasov-Poisson system are obtained in both the plasma physics and stellar dynamics contexts. It is proven 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 of the system, a conserved quantity. In addition, an appropriate global existence result is proven for the linearized Vlasov-Poisson system and the existence of stationary solutions that satisfy the above stability condition is established.
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Rigorous results on the stability of stationary solutions of the Vlasov-Poisson system are obtained in both the plasma physics and stellar dynamics contexts. It is proven 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 of the system, a conserved quantity. In addition, an appropriate global existence result is proven for the linearized Vlasov-Poisson system and the existence of stationary solutions that satisfy the above stability condition is established.
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Batt, J.; Rein, G. (Muenchen Univ. (Germany). Mathematisches Inst.) & Morrison, P. J. (Texas Univ., Austin, TX (United States)).Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions,
report,
March 1, 1993;
Austin, Texas.
(https://digital.library.unt.edu/ark:/67531/metadc1447750/:
accessed June 4, 2024),
University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu;
crediting UNT Libraries Government Documents Department.