Non‐linear stability for the Vlasov–Poisson system—the energy‐Casimir method

Source abstract

Abstract The problem of stability of stationary solutions of the Vlasov–Poisson system has received a lot of attention in the physics literature, both in the stellar dynamics and the plasma physics cases. The energy‐Casimir method has been used to prove non‐linear stability for various conservative systems, but no rigorous application to the Vlasov–Poisson system has been given yet. We employ this method to prove non‐linear stability of stationary solutions for the plasma physics case in three geometrically different settings.