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Nonlinear stability for the Vlasov-Poisson system – the energy-Casimir method. (English) Zbl 0814.76094

Summary: The problem of stability of stationary solution of the Vlasov-Poisson system has received a lot of attention in the physical literature, both in the stellar dynamics and the plasma physics cases. The energy-Casimir method has been used to prove nonlinear stability for various conservative systems, but no rigorous applications to the Vlasov-Poisson system has been given yet. We employ this method to prove nonlinear stability of stationary solutions for the plasma physics case in three geometrically different settings.

MSC:

76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35Q60 PDEs in connection with optics and electromagnetic theory
82D10 Statistical mechanics of plasmas
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