Abstract
We prove that there exists a class of solutions of the nonlinear Vlasov–Poisson equation (VPE) on a circle that converges weakly, as t → ∞, to a stationary homogeneous solution of VPE. This behavior is called, in the linear case, Landau damping. The result is obtained by constructing a suitable scattering problem for the solutions of the Vlasov–Poisson problem. A consequence of this result is that a class of stationary solutions of the Vlasov–Poisson equation is unstable in a weak topology.
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Caglioti, E., Maffei, C. Time Asymptotics for Solutions of Vlasov–Poisson Equation in a Circle. Journal of Statistical Physics 92, 301–323 (1998). https://doi.org/10.1023/A:1023055905124
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DOI: https://doi.org/10.1023/A:1023055905124